Gryphon

In my limited experience, I do not worry about closing the gap between the rings. The most important issue is that the scope does not move in the ring even if you are using a big caliber with heavy recoil. Tightening the rings too much & seizing the power ring is obviously not desirable.

I have used shims in the bottom to clear a low ring set on a BLR 358 Win (good recoil). I just cut out an old credit card & sanded the surfaces to make it rough. You can actually buy shim paper that is designed for scope shims (I do not know where you get them.)

I would also change the screws to Allen key type or the Leupold star key type & make sure that I do not over tighten the rings. That might just solve your problem without having to change your bases & rings.

I have the Australian Hilver bases & rings on my Simson 9.3X62 & they work fine. I understand that Lynx & Tasco are the same as the Hilver.

Good luck & good hunting.