Shimming is also a good way to get ring marks, because if one ring is higher than the other the scope rides on the edges.
I do a version of what Mule Deer recommends with duct tape. I just put a piece of tape in the bottom, but not all the way around. Then I test fire. If all is good, I put epoxy in the ring bottoms and use a precision steel bar instead of the scope, release agent as appropriate. After the epoxy sets, I peel the tape out and fill the remaining gap with epoxy, placing the bar as before. If done carefully, you end up with perfect stress free scope contact in the rings. No metal removal is involved, and the epoxy can always be removed with a good solvent down the road, if desired.
This is what I do if Burris Signature rings with inserts aren't applicable. Works well for me.
Paul
That's if the rings were aligned and you shim them out of alignment. It seems that if he runs out of vertical adjustment then the rings are out of alignment already, and shimming would be bringing them in.
