I have seen articles where different stock screw torque levels would help tune the Savage.
Working on memory here (and I have CRS) I seem to remember the front action screw is torqued with a torqueometer first and then the rear action screw is tightened in steps.
I guess the place to start might be 50 inch pounds on front screw and 20 inch pounds on rear screw and shoot 3 and see. Then increase torque to 25 inch pounds, 30 inch pounds etc.
I had a Savage Scout in 7/08 and the rifle was extremely senstive to stock pressure if a Harris bipod was mounted. In order to get repeatability I had to adjust the rifle to where it had a natural point of aim and then very gently reach up and grasp it without disturbing the natural lay of the rifle POA.
Thusly I could keep it in a steel target cut to E silhouette dimensions and 635 yards. If I just grabbed it and tried to control where it pointed resulted in wild shots. I just saw a couple weeks back the same thing occur in a Savage 22-250 with a bipod and I knew the rifle was capable of 1" at 200 yards.