DED; I believe you can purchase new, properly headstamped cases and ammo. The .44 Colt CASE is basically in the same family, size wise, as .44 Russian,(.97"), .44 Spl. (1.16"), or .44 Rem Mag. (1.29"), but each has a different length. .44 Colt is 1.10" in length.
.44 Colt cannot be made from .44-40, nor vice-versa.
In addition, the rim of the Colt round is narrower at .483. Historically the rims were minimized to fit in Colt and Remington cylinders of limited size when the original conversion work was done.
I'll let others advise you on what fits on what. Review these threads, as this is a FAQ.