It's been a long spell since I looked at an M1 out of the stock but I suspect a little Acraglas would be the best fix. There should be a recoil lug of some sort. Might need to actually remove a little wood and create a tighter fit.
You'll get a much more perfect fit than any sort of shim etc.
One must use caution not to create a mechanical lock and glue the action into the stock but it's not difficult.
In Memory of Paul "Dietrich" Stines.
Dad: Say something nice to your cousin Shirley
Dietrich: For a fat girl you sure don't sweat much.
Cue sound of Head slap.
RIP Muggsy & TMan
"If you are a warrior legally authorized to carry a weapon and you step outside without that weapon, then you become a sheep, pretending that JOCKO will not come today."