I'm not sure there is a satisfactory solution to your problem. If you use higher rings, you'll end up craning your neck to see through the scope. I had to use a lace on cheekpiece on my 21H 7X64 Brenneke, in conjunction with the pre-existing claw mounts, and that's not too cosmetically pleasing.

On my 22F 6.5X57 I mounted a Lyman All American Perma Center 4X in Warne mounts and only the slightest modification to the bolt handle allowed it to function. I had planned on using a Unertl Hawk 4X scope, but was stymied by the diameter of the ocular lens, which is far smaller than the one you describe.

If you are determined to keep the bolt handle unmodified, I'm afraid the only practical solution is to go to a scope with a smaller ocular lens.