Interesting carbine.  The M1886 carbine was standardly produced with a carbine buttstock and carbine buttplate.  I have seen M1886’s with special order rifle buttstocks (and they lettered).  It’s also not uncommon that buttstocks got swapped as a M1886 rifle buttstock will readily fit on a M1886 carbine.  If your carbine is original, I think it would be quite uncommon as I have never seen a rifle buttstock on a .50 Express carbine.  As right as it might appear (e.g. consistent overall condition/wear) you will likely not be able to convince a collector it is original.  Have you taken the buttstock off?  I would be curious if there are any markings on inlet for the upper tang or on the metal on the right inside of the tang.  I’d also take the forearm off to see what markings are on the under side of the barrel.

All M1886’s (carbine or rifles) in .50 caliber took some additional manufacturing steps (e.g. machining of some of the internals of action, as well as the breech end of the barrel) for the big .50 caliber cartridges to cycle through the gun and feed into the chamber.  If I had your carbine, the first thing I would do is check to insure .50-110 cartridges would feed and cycle through the action.