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One could put elec-tape on the rings, so as to not f-up the scope in case you want to change things. I put a layer of scotch-magic tape on rings so the scope doesn't get scratched. It compresses very well but adds a bit of a cusion.
Try a brass slim shims ultra thin we use them on bearings when the shafts are thin oh we know this thread is old maybe someone needs a tip hope it helps other wise you may have to call MacGyver