I mean the revel Constitution did a pretty good representation of the stern from the Peabody model so who knows maybe someone did some research and what they came up with was off some info I haven't found yet. Main thing is that these ships changed all the time so we will never know all the subtleties of these changes but we can extrapolate some of the evolution based on conjecture and available info.
United States’ stern was probably refitted identically to the other frigates in post-war refits. It’s an extensive one with the entire stern structure replaced. Earlier American frigates had excessive stern overhang, which could lead to pounding by the water in certain conditions. HMS Chesapeake’s commander once noted it was bad in the ship’s log.
The Java design during the war improved on that with a nearly vertical snub tail. Along with that there were three notable improvements to the tail design. First is the obvious increase in stern firepower, from four ports to six. The second is the vertical nature of the stern. This makes it much easier to shoot a cannon out of rather than the sloping ones previous. Finally, the whole structure is a heavier design as seen in the photograph of Constitution undergoing refit, compared to standard frigate designs. I think it’s pretty likely that the stern chases Constitution and her sisters engaged in, which included Constitution’s own stern chasers damaging herself, were a big influence in this new stern shape.
The Revell stern is almost certainly just a modified Constitution, I wouldn’t put a lot of stock in it being close to the historical design, nor a lot of the period paintings and etchings by someone who wasn’t there or hasn’t seen the ship in person. A lot of the reconstructions with Chapelle, the model, etc, all tie in together and are based off one another. If you look closely in that last painting, the stern seems to rise at the same angle as the Java’s stern.
I’m attaching a quick chart I threw together of some of the basic frigate sterns in the USN. You can compare the overhang and slope of the sterns in the older ships to the snub-nosed Java stern and interiors. Note also the reconstructed poop deck, rail, and hard-to-see upper galleries Chapelle did on the original Constitution design. Note also that President is shown with the diagonal riders, but there’s no evidence they were there when the ship was taken, if she ever actually had them (President was the lightest and fastest of the three).