My first recommendation is make sure you use good rings and bases. Dual dovetail to be exact. When I first got my 338 rum, I sheared the windage ears off of two sets of leupold rings before I went to dual dove tails. I got very good accuracy with just bedding my bdl stock and adjusting the trigger. Later I did add a break that helped a lot with my left shoulder. How much did you have to pay for your guns?
Remington model 700 300 RUM LH 26" rem ss/blued receiver lam stock 215 Berger @3025/180 NAB @3300
Remington model 700 338 RUM LH 27" Broughton 5C 225NAB@3300 /300gr Berger@2830
Savage LH 22-250