I vote for getting a bunch of 22s and practicing with your 10-22.
Most all rifles are going to "walk" when the barrel gets hot (there are exceptions). What happens is, with heat, the barrel expands and starts hitting the stock in different places.
Think of the barrel as a water hose. Water comes out and the hose flips around quite a bit. Touch any part of the hose and it starts flipping different causing the water to hit a different area.
Something you might try is to float the barrel of you Ruger American. Meaning, just in front of the action, use sand paper to open the the barrel chamber to the point you can slide a dollar bill between the barrel and stock, from the front of the stock to the chamber.
Buy new rifles is fun, (heaven knows I buy enough of them) but I really don't see it changing your problem. It may, but you may have to buy a lot of rifles to find out.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071