I think I would call it a .44 Extra Long / 444M Short??, with the 454 Cas. as the 45-70 Short.
Oh well, at about the same dia. and bullet weight driven at a similar velo they should all do the same job no matter what we call 'em.
Glad you got that shooting, maybe try some 44Mag based loads in it to see if it works as well as the 357Maxi's do with shorter cases.