The .44-40 is a bit of an anomaly - it's a Model 94 Winchester. Dad had picked up a Model 94 in .30-30 around 1980 or so, and years later learned that some were sold in Canada in .44-40. He located the parts, and installed them. I later added a Lyman 66 receiver sight.
I slugged the bore today, and found it measured .4295", so .44 mag pistol bullets should work fine in it. Guess that will be my approach