My M1 is a late 1943/early 1944, I believe with a 1950's barrel that looks new. As was it got about 4" groups with Korean ball. Did the following:
Used the instructions on the Fulton Armory site to polish the trigger.
Lightly(emphasize LIGHTLY) peened the barrel splines to get rid of some looseness in the gas cylinder/front sight assembly.
Made sure the handguards, front and rear, had just a bit of play front-to-back, not tightly fitted.
And cut two shims to fit on the stock where the floorplate bears to tighten the receiver/stock lockup.
After those things, with the same ammo gets 2" groups, sometimes a touch better on a good day for me. One of these days I'll get some match bullets and do some loading...
Oh, if you do want to hunt with it, you can get clips that only hold 5 rounds.