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They are full floated stiffineng will do nothing. The problem I have with my Savage 10 is the dang action screws keep working loose after it has been fired a while That effects accuracy BIG TIME.
It sounds like your action, including the recoil lug, needs bedding. You can roughen up the surface of the stock where the action sits, drill holes at angles. Clean with acetone and put a skim coat of epoxy bedding compound in the stock. The holes are to allow the epoxy to seep down into them and provide a mechanical hold on the epoxy, if and when it no longer sticks to the plastic stock. It's not perfect, but it works.
Does your gunstock have pillars? If so, they should help if the action screws are tightened down. Of course, I have seen some Savage stocks where the pillars did not run the full length between the action and the trigger guard. Those should probably be replaced with ones which do.