The way most cadets were converted to 32-20, was by grinding off the face of the breachblock until a cartridge would chamber. They were able to do his because the 310 had a "heeled" bullet so the chamber had no shoulder at the end of the case.This way would not be possible in a double rifle. As 1cdog pointed out, there is a consideable differance in diameter between 310(320+) and 32-20(311+).The proper answer is to load 310 ammo. Cases are easy to make from 32-20, and there is a bullet mold for the proper "heeled" 120gr bullet avaliable now.If you just absolutely refuse to make the cases and bullets(that is where the fun is),Buffalo Arms has both at a reasonable price.
Mike