I will second the little Russian bullet, CW, as it worked great in a Martini Enfield AC carbine (Enfield conversion from 450-577 to .303) I had a while back. I made 1250 to more velo loads with it, and other than sight changes, it worked fine in that .303 barrel/twist.
FWIW, were I doing this stub, I would NOT use a barrel with the old, original twist for the 32-20 (too slow); been down those roads before.
But, since I can download a 30-30, or 308, etc. to 32-20 ballistics, and the little 32-20 brass is fragile, and is slightly bottle neck, thus not an easily reloaded with carbide dies cartridge, I would look at the 32 H&R Mag or .327 Ruger, if I just had to have a 32 again.
As it is, I went to the 25-20, played with it and have ended up now with the 25-35 (same bore, faster twist). I can shoot cast or jacketed, short or long, with a better ballistic bullet.