I would take dowel rod to the size needed, glue in, then "screw it "
Forget the epoxy....too much monkeying around.
What I have done many times....(it works).
Take the recoil pad off.
Take a small piece of wood, preferably a softwood like cedar or pine.
Take your knife and fashion what is essentially an over-sized tooth pick that is the correct size to fill the hole in the stock where the recoil pad screws go. Long and slender, not short and fat.
Now, take your over-sized tooth pick and tap it into the hole until it stops.
Now cut it off flush.
Re-install the recoil pad.