Paul,
Your note
"Actually, if it wasn't for the barrel ending up being too thin when converted to .32 Winchester Special"
As I stated, the 32 Win Spl base is the same as the 225 in diameter. However, the 225 is rated at almost twice the pressure of a 32 Spl. The Cadet barrel is not too thin when chambered for the 32 Spl or the 225.
The only round suitable for the rechamber and use of the original barrel is the 32 Win Spl. However, the twist of the original 310 barrel may be a problem, due to bullet weight differances. I would suspect that the heavy bullets of the 32 Spl will not stabalize.
Before I put money into the old barrel, I would just rebarrel the beauty and chamber it as you want, for a more modern cartridge, that did not require head stands to make work.....
Ed