I was gonna suggest this one too. I always use a shim of electrical tape to protect the scope. If you cut it precisely, the tape can't be seen once the scope is installed. It's not that this is a fix for your problem, this is the best way to mount a scope. The tape not only protects the scope, but also creates more friction and makes it less likely that the scope will shift. I've had scopes on guns for decades without ever having zero to shift using Scotch brand electrical tape inside the bottom and top of the ring.

I didn't think this up myself; I first read about it on the old TC list back in the 90s. You can get higher rings if you want, but you could actually have a superior setup if shimming with tape gets you clearance. I've always wanted my scope as close to the barrel as possible without touching it, and it sounds like you only need a little more clearance to have that with the rings you already have.

Also, if you have clearance before tightening the rings, you oughta still have clearance after tightening unless you are torquing the scope. I would take it off, place tape under the rings, and then carefully tighten them. Turn the screws down evenly, constantly rotating front to back and left to right as you do. I'm thinking this will get the scope as close to the barrel as possible without touching it, and that's the best setup. Good luck with it