The only reason to add a shim is when the saddles are bottomed out or to increase break angle over the saddles.
If you put a shim in, you'll have to raise the saddles to get you back to your action at 12 but the heel won't have changed. You see?
This just sounds like you have too much relief to me. .
'73-4 Ampeg V4B, Ampeg PF350,PF115HE, PF115LF, 115 Traynor, 1962 Fender Jazz, 75 Gibson G3, '10 Squier VM Jazz, Squier CV 60's P Sonic, Squier CV 50's P blonde, Epiphone Thunderbird IV