I would have thought that the 44 Remington or 44 Colt would be the most likely cartridges for a Remington Army conversion cylinder, but then I don't know all that much.
Since the frame appears to be (mostly) unaltered, you could still use a percussion cylinder in it. The rear corners of the cylinder cutout in the frame appear to have been squared off for some reason - maybe part of installing the conversion cylinder? That seems odd to me.
That cylinder pin should not be coming clear of the frame with the loading lever installed like that. Or maybe that's not happening, and you just took the photos that way, and you had to remove the lever to get the cylinder pin back in.