I would try the Burris Signature Zee rings. They have really nice plastic inserts that allow you to align the scope better without using a lot of the scopes internal windage and vertical adjustments to do it.
Sometimes the base mount screw holes, on to of the action, are not well aligned with the barrel. This can cause excessive use of the scopes internal adjustments to correct it. The Burris Signature Zee rings correct this. They also allow you to add extra MOA to the vertical adjustment, much in the same way as a 20 MOA rail does.
I like to use a little dusting of rosin, like baseball pitchers use, to help rings grip scopes, I do this on regular rings as well as the Signature rings.