I would fix what is wrong and change NOTHING else.
I don't know why you'd be told to "shim" anything. Whatever has happened to your accuracy can be brought back to "normal" again by reversing whatever happened. I'm still betting it's the scope mount screws or possibly the scope's crosshairs have gotten loose... and are moving around inside the scope. I've seen that happen as well, but that's a rare happening, but also a possible reason for the poor accuracy.
I'd first check the scope mount screws for tightness.
As a last resort, I'd install new mounts... but I doubt that the scope mounts, themselves, are the problem. Scope mounts do NOT "wear out".
Good luck!!! I know how frustrating such problems can get... most of us have had to go through such problems with our "pet" rifles as well. Such things can and do happen if you hunt long enough with the same rifle.
I had one of the scope mount screws break off causing a 2nd mount screw to loosen up after many years of use on my Model 70 in .338 Win. Mag. that I bought in 1961. I had the front scope mount screws loosen up on the scope mount of my 1953 Model 99 Savage in .300 Savage caliber (the forerunner of the .308 Winchester cartridge) I bought as a replacement for the Model 70 (just too much recoil for an aging hunter who likes to do a bit of bench-rest shooting in the off-season) which I can shoot all day long off the "bench".
The Model 99's scope mount screws loosened up after many, many years of having the same scope mounted on the rifle and literally HUNDREDS of rounds shot down the barrel.
As you can see, these things just "happen", but don't go off "half-cocked" and make a bunch of changes in your rifle...
i.e., don't "fix" what ain't broke. If you change things that aren't the original problem, you may end up making your fine rifle LESS accurate than it would have otherwise been had you simply tightened up the scope's mounting screws (if that is the actual problem).

Strength & Honor...
Ron T.