My bet is Scope failure or scope base issue.

Often times the screws for the front base are too long and they bottom out before they actually tighten on the base itself. So you think its tight, but its not.

If all that checks out then as mentioned above check the tang for float. With a Remmy there is a screw there so you would want it bedded or at least snug, but on a Savage the screw is well ahead of it and long story short it can cause action pressure point issues and can cause problems.