No, the inserts are quite thick, spherical on the outer surface so that they can swivel like a gimbal inside the rings. Won't fit another type of ring.
I think you will probably be happiest with a new set of higher rings to gain the clearance. In my opinion, you need scopes mounted in a solid, foolproof manner.
Burris rings of that style are around $60.00 a set. The straight Zee's are cheaper, but don't use the insert.