If the .32 is loose, the next logical thing to expect to find, given its age, is a .36 of some kind. The .38 Special came to mind right away, as Jim suggests. It is a bit shorter than the original cartridge and a little fatter, having another 30 mils in the case body and rim diameter. The 32-20 rim is just big enough that it wouldn'f fall in, but if its case didn't rattle loosely in the chamber, I don't know of anything with a bigger bullet and a case that narrow? Perhaps someone wildcatted the 32-20 up to 38-20? Since the .32-20 case diameter is O.D. is only .354, this would involve a special bullet with a rebated tail, like a .22 rimfire bullet. You could try dropping a .38 special dummy in the thing see if it fits? Unfortunately you will need to do the casting to learn anything more?
The other odd possibilities that occur to me would be the chamber left in 32-20, but the bore opened up for the 32-40 Ballard bullet. At .321" that bullet is just enough over the 32-20's .3125" that you could drop the latter into the bore diameter of the former. You might be able to seat without case mouth expansion. Short case life, but not entirely out of the question.
It could be opened up for a .338", for that matter, but you would have to expand the cases to seat them, for sure. Be about as much fun as the theoretical .38-20 I mentioned earlier, but avoiding the custom bullet mould.
I think I've talked back around to the casting.
Nick