Hi Julie Mo. The Byrnes saw does a great job ripping 1/42" veneer.
I start with a zero clearance insert with a fine tooth blade and a metal ruler clamped to the fence to stop the veneer from sliding under. I also removed the blade guard and use the end of it keep the veneer from riding up the blade.
This is the blade I used. It's 63mm (diameter) x .2mm (kerf) with a 16mm or 5/8" arbor. You also need an arbor adapter that you can buy from Jim.
The strip is 2 mm wide. I don't get any binding doing it this way. I'm using a slitting blade so the teeth are the same kerf as the blade part, so the blade isn't necessarily the problem you're facing. Are you using anything on your fence so the wood doesn't get under?
Here is a pic of the two ends together to show the accuracy across the length of the strip.
The saw can cleanly cut miters even on a strip this small.