I agree with all the above, but I would surely check the bases, WITH THE SCOPE REMOVED FROM THE RINGS. I have seen too many things overlooked by others (myself included) to assume they have it right. SOMETHING is wrong, either the scope is moving in the rings, or the bases are moving, or the scope is bad.

Should we ASSUME you're not flinching, as well? I have a 338 WM, but have as yet to fire it. I do hear the recoil is pretty fearsome. I realize the 300 RUM is no lightweight either, which is why I hesitate to ask, but just trying to eliminate all possibilities.