A friend of mine, who is a new shooter, brought one the Commemorative issue levers (Cheyenne carbine?) to the range for a trial run. He was using Winchester factory fodder (200 gr copper jacket rifle ammo). Well - the thing shot horribly - couldn't hit a large pizza at 10 yards. I checked the obvious - loose sights, loose barrel, ringed bore, dirty bore, etc, with nothing to show.
I know squat about these rifles... Anybody have any experience with these rifles and caliber? One thing I did note is that the rifling seemed to be very shallow. Perhaps these rifles are sensitive to bullet OD and composition?
Obviously, without examining the rifle, it's pure speculation.
However...
The bore is probably rifled for .44 magnum, which is .429" groove diameter, while .44-40 is a .427" groove diameter.
The .429" rifling set-up was probably more convenient and cheaper for Winchester to use, and they didn't worry about commemoratives being shot anyway. It's a safe compromise, if not an accurate one.
This, combined with very shallow rifling would probably account for bullets not gripping the rifling properly.
I had a Rossi 92 in .44 magnum years ago, which also had abysmally shallow rifling. When I tried lead bullet reloads at .44-40 velocities in it, they key-holed at 25 yards.
This rifle had the typical 1:28 twist typical for .44-40 rifles, so I concluded that the shallow rifling was at fault. Perhaps using .431 diameter bullets might have helped, but by then I was fed up with it.
You should first slug the bore, as had been suggested to confirm if it is .429".
You could then try getting some .44-40 reloads made up using .429 JSP .44 magnum bullets. If they will chamber, the accuracy might improve.