I am much more of a lurker on this site than an active commenter, but that butt plate looks pretty similar to those on AH Fox shotguns. CSMC sells modern reproductions of Fox shotguns. The reproduction butt plates are made of the same material originally used on the old guns. I bought one of Galazans Butt plates from CSMC to repair my butt plate on my A H Fox (Grade A made in 1927). I had to learn to gently heat the material to better fit the slight curve of the butt stock.That can be done in heated water or with a heat gun (be gentle) However, after messing with it and getting the curve correct on the plate, I simply sized it by hand using files and sand paper while I had the Fox butt stock taped off. (Theoretically, it can be done on a belt sander ...but I wasn't risking damage to the stock by sanding too aggressively.). When completed, polish the sanded edges. FYI, I have fit pads to modern shotguns before with a similar technique. It turned out great. Not only does it look original, it fits flush and perfectly. I think the plate was only something like 20 bucks or so plus maybe shipping (it has been probably 10 or more years....keep that in mind). You will have to measure all the butt dimensions plus the hole spacing before ordering.
Good luck. Beau