An excellent solution to the problem is to replace the Weaver rings with Burris Signature Rings. The ring inserts can be replaced with offset inserts (without putting ANY strain on the scope) and you can, depending on how much offset you select, get major sight changes. Then, you can fine tune with the scope adjustments.
I have used these on a number of rifles and pistols that I have scoped.
The base must allow the use of standard Weaver Rings and you must get the "Weaver Style" Burris Signature Rings.
They are not terribly expensive either. They have more holding power than standard rings and will NOT mark your scope.
One caveat - the inserts are polymer, and can creep a bit after they are first tightened. The solution is simple, just re-tighten them the next day. Then, they are good!
Dale53