If you bed that action, and it turns out that the barrel is a lemon, I don' t think that Savage is going to back you up. I would keep it in original condition.

The Savage model 11 is free floated but not pillar bedded.
I have a couple of these guns. My 243 will shoot 1" groups, but ONLY with a certain factory ammo. The other ammo will shoot under 2 and 1/2" though. My model 11 in .308 will shoot under 2" with the cheapest ammo that wal-mart sells.

I would bet that the problem is the scope. Unless you know for a fact that this scope is PROVEN. I have had this problem before with a Remington 30-06. Some guy said that the scope was " good." I put the scope on another rifle that would shoot any ammo accurate, but with the " good" scope, it would only get 6" groups.

Prove to YOURSELF that the scope is good.