@longcruise ,
Thank you for your comments. I think that gun in the "collage" of photos was re-stocked, using most of the original hardware, likely by a gunsmith at one of the frontier trading centers. James Josiah Webb, a Santa Fe trader, reported that his rifle had been re-stocked at Bent's fort, and Lewis Garrard stated that his rifle had been re-stocked by "an enterprising Dutchman" with limited tools on the frontier. So, we know this type of work was done.
Looking at the Barnett gun, I agree with you about the buttstock. Other unusual features are the absence of the "baluster wrist" that was always seen on English trade guns, as well as on the Brown Bess. The subject gun has what I would describe as a simple "shotgun butt." The buttplate on this gun appears to have more rounded corners than you normally see on Northwest guns, and frankly it looks more comfortable. I think somebody either "improved" or replaced it. Finally, the carving around the lock looks very crude to me, suggesting the possible re-stock was done by someone competent but not a master of the craft. Maybe a blacksmith who did some gunsmithing when necessary. Northwest guns were relatively cheap, but they weren't this crude. I'm not certain of the wood on the Barnett gun, either. It doesn't look typical to me. Maybe a local Canadian wood like birch? I can't say.
It is an interesting gun!
Notchy Bob