two surefire ways without altering your rig. one... use locktite behind and along both mounts. two... switch to kwiksite mounts, they use four screws in the top and therefore, they are wwiiiiiidddddeeeeee, with lots of surface area on that edge grabbing on. I use them on everything , including a post ww2 parker hale 308 ultralite. All other mounts and rings used to dig trenches in my scope, once i put those on, problem stopped. This is on a 308 that ,with scope, doesn't weigh 7 lbs.
A third way , if you don't mind a high setting scope, is to get the kwiksite, weaver style, tip-off block mounts. Put those on first, they don not move, then put on any rings you want.