Something sounds wrong. You say a "new" scope. Does that mean you had another one which you could get a 100 yard zero & was more or less centered & w the thimbles? Or is this the first scope.
You can shim bases, but there are limits, and you can stress the scope. Easiest would be to get the Burris rings that have inserts. These will give you a lot more adjustment, and not stress the scope. But since something sounds wrong, even the 20 MOA available might not be enough.
Best would be to have a gunsmith take a look & fix the problem. I know it cost money, but if you plan to keep the rifle, it is always best in the long run to have things as they should be.
Good luck