A puzzle to be sure.

The barrel, though "wrong", looks to have been there a LONG time. The sight appears to be quite a bit more recent, and the screws, especially the rear one, do not look to be TD screws? Who knows how it came to be, over the last 144 years?

It will look great on the wall, though. If it were mine, I'd look long and hard for a bar & ring, and a rear sight (probably an 1879) of JUST the correct patina - NOT to try and pass it off as a 1st model, at all, just to make it a bit more complete.