I haven't been to Salem for quite a few years. (My wife and I may get up there this summer, in which case I'll take a good, long look at that model again.) I have, however, studied the old model fairly closely, if informally, several times, and studied pictures of it. Take the following with a grain of salt; if somebody who's seen the model more recently contradicts my recollections, that person is almost certainly right.
To my eye, the model gives the distinct impression of having been built by more than one person. The rigging is extremely well-done, with excellent, scale-looking splicing, seizing, etc. The rest of the model, for the most part, is downright crude. The basic shapes are about right - but that's about the best that can be said for it. The gun carriages, for instance, are crude chunks of wood with no attempt to represent the carriage trucks or any other details. The gun barrels are extremely simple turnings - maybe made on a simple furniture lathe, but most likely, I think, whittled out of sticks. They're tapered a little, but have no bands, cascables, or other details. And each gun is held in position by a great big nail, with its head showing on top of the gun barrel.
The deck furniture is equally primitive. My theory is that the absence of the steering wheel, bell, and other details is due to the modeler's inability to make them. (Even on such a large scale, making a double steering wheel is quite a project, and I don't think this guy had either the tools or the skills to do it.) The decorations on the bow and stern are so crude that it's difficult, if not impossible, to give them any serious interpretation. And if I remember correctly the modeler made no effort to plank the decks to scale; they consist of wide sheets of wood, even lacking any scratches or grooves to suggest the edges of the deck planks.
I have the impression that, at one time, somebody at the Peabody Museum (as it was then called) took an interest in the model and did some research on it. Whether that research included "forensic methods" I don't know. Frankly I doubt it. I have no trouble believing that the story of the guns being fired is mythical; I certainly didn't see any evidence of such behavior. And the idea of such tiny wood guns being loaded with gunpowder and fired stretches credulity a bit. (But then, maybe the original guns were metal....)
The Peabody-Essex Museum is a fine, professionally-run institution. Somewhere it must have a file of information on that model - though how much information that file contains I have no idea. (An artifact file in an American museum may contain one or two sheets of paper, or may be several inches thick.) Nor do I know how easy or difficult it would be to gain access to that information. The amount of effort that modern museums can put into answering queries about such things varies tremendously from institution to institution - and from time to time. (When I was working at the Mariners' Museum, our policy was to answer mailed queries as best we could, subject to reasonable time limitations. Anybody who sent the Mariners' Museum a letter about a model or a painting could figure on getting a letter back from a curator within a couple of weeks, at the most. And if an individual actually showed up at the museum with a question, we literally dropped what we were doing in order to answer that question as thoroughly as we could. The MM abandoned that policy a few years after I left.)
I don't know what the Peabody-Essex Museum's policy about queries from the public is, but, as we've noted in another thread, maritime-related artifacts like that old model don't seem to be getting as much attention as they used to get. I'll repeat my earlier comment: the "Hull model" really deserves to be the subject of a published monograph. But I'm not optimistic that such a book will appear in the near future.
I feel like I should emphasize again: I haven't actually been in the same room as that model in several years. If anybody who's seen it more recently has something different to say about it, that individual's observations probably are more valid than mine.