Not a Mosin-Nagant rifle, but an 1895 Nagant pistol - the gas-sealing revolver.
You can apparently shoot .32 long rifle in it, especially with a slightly different cylinder (because of the scarcity/expense of 7.62 nagant ammo)
I seem to remember that the original case was longer, and that the bullet was seated completely inside the case mouth. When the cylinder was levered forward, the brass case actually formed part of the seal. Does your examination of the gun bear that out? I don't think I've ever handled one myself.
I also seem to remember that it was possible to form brass out of .32-20 brass, but that the case wasn't quite long enough. It would work, but you wouldn't get the gas seal.