Jaager

For POF trunnels can add significant hold strength.   There are many contemporary models that use either brass or wood and some with both.  The diameter is out of scale.  No reference to support this, but I think that the choice of glue then was hide glue.  It would likely have been either a home made extract or a cottage made product - no QA.   Both English and French built models have doweling.  The patterns and numbers match full size requirements.   My money is on there being method behind most everything the old guys did.  It was a professional and shop built operation back then.
 
Pins and trunnels can be effective clamps also.  Although using bamboo trunnels to hold wet planks down can be tricky.  Some species of bamboo are strong and hold up to push pressure.  Some species are not so strong.  They bend  and crack.  The perverse aspect is that the softer species are much easier to pull and have a higher yield.  A high speed electric drill with industrial HSS bits of standardized diameters probably makes this much easier for us.    

It is my guess, but perhaps Franklin was first on the market with yellow PVA and it gained enough of the market attract competitors.  Effective advertising and placement in how-to magazines did the rest.
 
As for the rubber cement - Over time the bond will fail. No surface treatment is likely to save it.
Bamboo dowels may, but there is not much backing support for them.  The wood species makes it more decorator than historical, so even brass pins could enhance the presentation. There is still the problem of not enough support thickness.
 
A more permanent  solution may be to number each plank.  Treat the hull with n-Hepane to solubilize the rubber cement.  Remove the planking.  Clean all surfaces of cement.  Then reapply the planking using PVA.
 
The re-application processes is a lot like the kit coming with pre-cut and pre-bent planking. Except that instead of a computer guided laser, it is a human guided tool.

It is my guess, but perhaps Franklin was first on the market with yellow PVA and it gained enough of the market attract competitors.  Effective advertising and placement in how-to magazines did the rest.
 
As for the rubber cement - Over time the bond will fail. No surface treatment is likely to save it.
Bamboo dowels may, but there is not much backing support for them.  The wood species makes it more decorator than historical, so even brass pins could enhance the presentation. There is still the problem of not enough support thickness.
 
A more permanent  solution may be to number each plank.  Treat the hull with n-Hepane to solubilize the rubber cement.  Remove the planking.  Clean all surfaces of cement.  Then reapply the planking using PVA.
 
The re-application processes is a lot like the kit coming with pre-cut and pre-bent planking. Except that instead of a computer guided laser, it is a human guided tool.

I put these in my garage / workshop and the amount of light is significant.
https://www.amazon.com/s?k=led+garage+lights&ref=nb_sb_noss
Maury

The timber efficient way on the original ship would probably have used six pieces of timber to make the rail.
It would still require spilling from wider stock and five scarphs.   Three hook scraphs - but for the two "v's"  I can't think of anything but a straight butt.
Given the mfg and the year of origin, the wood species that you are calling walnut is probably actually of African origin.  It is probably in the Mahogany family, open pore and brittle.   It probably does not want to bend thru the thin dimension, never mind bending thru the thick dimension - which also never goes well with any  species.  This one will probably split if you try to bend it in that plane.
Since you are going to need to obtain wider stock, why not use an appropriate species for the rail?   If you like the Walnut color - which would not be the color of the original, a dye can do it.  For a stain, Walnut is probably the most common shade.  You do not want to use a stain though,
 
On your JPEG #1 -  the pattern of the deck butts indicates that the designer of the kit was beyond incompetent.  The deck plank butt patterns in the 17th century may have been less regimented, but a butt on the same beam for every other strake is just wrong and ugly.

The timber efficient way on the original ship would probably have used six pieces of timber to make the rail.
It would still require spilling from wider stock and five scarphs.   Three hook scraphs - but for the two "v's"  I can't think of anything but a straight butt.
Given the mfg and the year of origin, the wood species that you are calling walnut is probably actually of African origin.  It is probably in the Mahogany family, open pore and brittle.   It probably does not want to bend thru the thin dimension, never mind bending thru the thick dimension - which also never goes well with any  species.  This one will probably split if you try to bend it in that plane.
Since you are going to need to obtain wider stock, why not use an appropriate species for the rail?   If you like the Walnut color - which would not be the color of the original, a dye can do it.  For a stain, Walnut is probably the most common shade.  You do not want to use a stain though,
 
On your JPEG #1 -  the pattern of the deck butts indicates that the designer of the kit was beyond incompetent.  The deck plank butt patterns in the 17th century may have been less regimented, but a butt on the same beam for every other strake is just wrong and ugly.

Rather than have the wood friction turn at the brass bars, the bars could hold a ball bearing race. They come in a wide range of ID and OD.

If you are only going to use it for spars and are not content to use the hand tool - square to octagon etc. method,  all that is needed is a motor to turn the stock.  If working the stock directly without a tool post or tool rest, a 1/2" drill will turn the stock.
Just build a jig to hold the drill on its back.  Another jig to hold an upright stick with a ball bearing race can support the distant end.
Unlike the sort of small lathe that you are evaluating, which will have a way that is shorter than most masts, a drill jig can have any length of one piece way up to 8 feet.  Ball bearing races come in a wide variety of ID  and shims can make up the difference.

This vessel was 1872.   Drake's first well was ~1860.  So it is entirely possible that petrol based tar was in use, so actual black for standing rigging may be appropriate.  The running rigging -a dark straw - likely hemp.  This was a privately owned two master, so I doubt that steel was even considered.
But as Gregory says:  you can do much better for the line that you rig with.

I have the plans from AAMM.  When I look at the plans, my evaluation is that there sure are a lot of guns!
It is kinda busy looking.  Given the year that it was built,  I think the design was based on an obsolete concept.   I think they are mostly close range shotgun type cannon.  anyone foolish enough to get close could get hurt. However,  not too long after, there would be very large caliber rifled shell guns on tracks at the mid line.  A corvette with two or three of those - -  smaller, faster, less expensive - and in a few more years add steam and this frigate may as well be a towed target.

https://boutique.aamm.fr/monographies/plan-belle-poule
 
Is this what you want?

The physics - the engineering characteristics - the strength - of wood has not changed over the last 2500 years.  The hull volume and length would determine most of it.  The warships would have to factor in the mass of the guns and the stresses produced by discharging them.  There were fads -  because they did not practice real Science for their inquiries and did not have any instruments that could measure the data anyway.  So from 1650 to 1860 at least - any variation in scantlings relative to and within a class of vessel size is probably difficult to observe - at 1:48 and smaller.  
 
Personal philosophy:
It is easy and probably natural to become hung up on what are insignificant differences.  A tendency toward obsession over minor details comes with this territory.  Letting a search for the Perfect become a blocking force field for getting to the Good - can be counterproductive and discouraging of an otherwise worthy project.  I am happy to have finally found my way out of that mental wilderness.

The physics - the engineering characteristics - the strength - of wood has not changed over the last 2500 years.  The hull volume and length would determine most of it.  The warships would have to factor in the mass of the guns and the stresses produced by discharging them.  There were fads -  because they did not practice real Science for their inquiries and did not have any instruments that could measure the data anyway.  So from 1650 to 1860 at least - any variation in scantlings relative to and within a class of vessel size is probably difficult to observe - at 1:48 and smaller.  
 
Personal philosophy:
It is easy and probably natural to become hung up on what are insignificant differences.  A tendency toward obsession over minor details comes with this territory.  Letting a search for the Perfect become a blocking force field for getting to the Good - can be counterproductive and discouraging of an otherwise worthy project.  I am happy to have finally found my way out of that mental wilderness.

The physics - the engineering characteristics - the strength - of wood has not changed over the last 2500 years.  The hull volume and length would determine most of it.  The warships would have to factor in the mass of the guns and the stresses produced by discharging them.  There were fads -  because they did not practice real Science for their inquiries and did not have any instruments that could measure the data anyway.  So from 1650 to 1860 at least - any variation in scantlings relative to and within a class of vessel size is probably difficult to observe - at 1:48 and smaller.  
 
Personal philosophy:
It is easy and probably natural to become hung up on what are insignificant differences.  A tendency toward obsession over minor details comes with this territory.  Letting a search for the Perfect become a blocking force field for getting to the Good - can be counterproductive and discouraging of an otherwise worthy project.  I am happy to have finally found my way out of that mental wilderness.

The physics - the engineering characteristics - the strength - of wood has not changed over the last 2500 years.  The hull volume and length would determine most of it.  The warships would have to factor in the mass of the guns and the stresses produced by discharging them.  There were fads -  because they did not practice real Science for their inquiries and did not have any instruments that could measure the data anyway.  So from 1650 to 1860 at least - any variation in scantlings relative to and within a class of vessel size is probably difficult to observe - at 1:48 and smaller.  
 
Personal philosophy:
It is easy and probably natural to become hung up on what are insignificant differences.  A tendency toward obsession over minor details comes with this territory.  Letting a search for the Perfect become a blocking force field for getting to the Good - can be counterproductive and discouraging of an otherwise worthy project.  I am happy to have finally found my way out of that mental wilderness.

Wonderful!  You have rescued the whole line...
 
Although, I am an antimatter analog to popular culture, not an author or draftsman,  I have been thinking of subjects for new title lines.
The 200th anniversary of the U.S. Ex.Ex.  is fast approaching.  Six vessels that represent the actual working vessels of the Antebellum USN.
There are plans for the others ships that were out there with them:  Astrolabe/Zelee.
Maybe the AOTS HMS Beagle can be rescued and actual physical plans be added.
Ships of the 1719 Establishment -  I found working plans for  100, 90, 80, 70, 60, 50, 40, 20 gun ships.
The HMS Prince - that was in the Science Museum for years - can be returned to the spotlight and a full monograph done.
 

Any chance of getting ghost writer or co-author to complete the series that Grant Walker bailed out of on the 3rd volume?

I was thinking that also acting as an overseas distributor might help, but about the only other publisher in English is Sea Forth.  A long paging thru NIP shows that they still are a US agent for them - slight as their output is now.  It sort of only leaves ANCRE as a possible partner. 
Anyway, it is a great service that you have taken on - keeping the SeaWatch titles available. 
Now, if only NMM would find someone better than DHL to get their plans across the Atlantic.

My guess is that the dark horizontal line is a wooden batten.  A spreader lashed to the shrouds  instead of a foot rope.
There could be a hole in it for the line, but I would scab a horseshoe shaped piece of wood at the back instead.  

You can also slide one of these thick razor-blades with reinforced back between the wood and the paper. That helps to peel it off, even when it has been on longer.

I have had excellent results using rubber cement.  I use a high quality brand - BestTest.  I apply a healthy coat to both surfaces - let it dry for ~15 min - then apply.  This is an instant grab- no adjustment version.  It will hold for a long time.  It just takes rubbing with your thumb to completely remove it.   I have a bottle of n-heptane - the solvent.   adding it to the cement bottle when it gets too thick to brush easily.
 
Plain paper can be a bit of work to get started to curl up - it will tear - the edge is a challenge to get under.  To make my patterns easier to remove, mostly immune from the effects of humidity, and protected from dirt and smudges - I brush a thick layer of brushing lacquer on the sheets. 
The solvent is fierce enough when brushed outside, I would never consider any spray version.  I overlap all four edges with 1/4" crepe masking tape because if the lacquer sneaks under the pattern and dries the patterns stick to the butcher paper they are taped onto.

Allan,
I get my answer for this from the contract for the corvettes Warren and Falmouth  included in the appendix of HASN.
i.e.  heart Pine, max 10" width, 2.5" thick, 40' long.
 
American as a separate entity was late to the game.  Before 1783 the RN was us.  I have read about there being lots of trees in the North American colonies having a brand with the king's symbol - which I think meant  - you may own the the land, but this tree belongs to the RN.  The Baltic gets the press as the source for Pine and Pine tar in books published after 1783, but before this, I think Georgia and Carolinas were the main source for a while.
There was a species of Pine that was loved into near extinction in the early 20th century.  It was a large tree, very tall and straight.  The grain was distinct, yellow and red,  the red was as hard as a rock.  It could turn nails. I think it would depend on when a "repair" of Constitution was done for them to use it.  The later, the less likely that it was still available.   
 

The following is speculation - I have no specific references, just years of reading:
 
The decking  - the probability is high that it was a southern yellow Pine.  
Working ships tended to have their decks subject to frequent sanding -  actual sand under a moving heavy flat rock.
No clear finish of any kind.  Bare feet react poorly to splinters.  These same feet tended to track tar, as well as it dripping from the rigging,  so a captain who wished to keep his command and or wished for promotion would keep the decks clean.
A varnished deck - more often wet than not - would be too slippery - they did not have TopSiders.
 
Consider a dose of 50% diluted clear shellac - and when dry, wait a few days and rub the surface with a ScotchBrite pad.
 
 
The wood Hard Maple, Birch, Beech -  To my eye the premium snow white Holly tends to be too white and I don't think any species of wood that gets large enough to build anything with is near that white.   But - I chanced upon some #1 common Holly at Advantage Lumber that was only $6.00.BF.  It is not white, the yield of usable product would likely be 50% at best.  But it what could be isolated would have the same wonderful Holly working characteristics.

Right. This is perhaps why Navy Board style models are so “sexy”…

I really can't draw.  If you look at most any NMM plan that shows the framing, it shows something like the following :
For a plan with a three bend station interval, there will be a bend with a frame on either side of the station line. (This is normal in most every case.)  But in between  there will be only one other bend. The rest of the area is filled with single filling frames.  The futtocks significantly reduce is sided dimension. They often jog so that they frame the sides of the ports so that they are not cut into.  To me, it looks like a cross between a plate of spaghetti noodles and 2x4 16" on center house framing.  
The NA/French is all bends, most all the futtocks have the same sided dimension - except maybe the tops.  The timbers are cut into for the ports.  The zone with cant frames is as small as possible. 
 
(On a model, I take this more efficient method one step further: I avoid cants altogether.  I do not mind cutting away a lot of wood, so I keep my frames square to the keel all the way.  At the last station forward, the bow/hawse timbers come in at 90 degrees (parallel to the keel).  At the stern, my last square frame is where the fashion frame would be.)  ( I think the stern framing is a bear - It does not matter how the rest of the hull is built - POF, POB, even carved - it is difficult.)
 
Most of my framing has been for all bends,  before about ~1770 it was about 2/3 timber and 1/3 space. Attractive to display.  Somewhere around 1770 the framing was about all timber.  The space was 1"-2".  Pointless to display.  Here is where the Hahn style of omitting every other bend makes sense.  This also really saves on wood.   Then some time around 1815 it went back to 2/3 timber and 1/3 space (on average).    I guess that it was discovered that all wood does not stop hogging and does not stop cannon balls and less space meant more fungal rot.
 
Of late, I now feel comfortable with a Navy Board style framing for vessels up to 1770.  True Navy Board framing has the floor timber extending above the turn of the bilge.  The shortened F2 is missing as is part of F4 below the wale.  F1 is much longer.  It goes from above the wale to a bit short of the keel.  It makes both timbers very long and very curved.  The plank that they are cut from has to be wide.  There is a lot of waste.   For a more efficient use of wood and to not need frame stock wider than 2", I alter the disposition.   I have a normal length floor ( ~ 60% of the breadth ). I have an extra long F2 that butts against the floor and goes above the wale.  (unlike the floor with a different curve at either end, it is a single curve, so it fits on a 2" board.)  For F1,  I use a 5'-7' piece that half laps the floor and F2.   It is either a short timber or a long chock.  The spaces are not staggered.  They are both in the F1 zone.  From a distance it looks the same as Navy Board - until you notice that the spaces do not stagger.  I get the look without the waste.  Oh, because I think it is ugly, I plank over everything from the wale on up.  Because it is covered, I use a solid wall of timber from the wale on up.   I also have a piece of deadwood between every floor timber.  From what I read, most ships also had this as a chock.  There was a 1"-2" gap above the keel so that water could flow across the keel from bilge to bilge,  A model doe not need the gap.