I recently solved a scope alignment problem by lapping. Lots of lapping.
It was for a Ruger No. 1, and Burris Signature rings weren't available.
I solved the windage component with windage-adjustable rings, but the elevation component would have required a 0.025" shim under the rear mount.
Rather than mess with the Ruger integral mount system, I chose to lap the front ring lower. 0.025" was enough that I had to take a little off the lower ring half "ears" to maintain a gap for clamping.
This maintained a "cylinder" clamp arrangement for the scope, so it didn't bend it.
IMO, any shimming, whether it is between the mount and the ring or the ring and the scope, has the potential to bend the scope tube...