According to gelatin tests posted on Tactical Forums by Dr. Gary Roberts, the best performing load should be the Remington 110 grain JSP, followed by the Winchester 110 grain JHSP. In his tests, the Federal JSP performed like ball, IOW, not good.
These tests were before the Cor Bon DPX load was available; I don't know how it would compare.
If I was going to use an M1 Carbine on southern deer, I'd use Remington JSPs and keep the range to 100 yards or whatever range I could consistently put all my shots in the boiler room, whichever is less.