You do not need to change scope bases. Burris makes their Pos-Align rings that will fit your Weaver bases. These rings use nylon insert bushings to eliminate alignment issues with scope mounting or off-center scope mounts. They also sell a bushing kit with offset bushings for about $10. The offset bushings will allow you to angle your scope with -20 moa in the front ring and +10 or 20 in the rear ring.