Sounds like you have Buehler Scope Bases and Rings - they were very popular decades ago - especially for the "big bores".

The rings should have spacers in them to fit the scope - important to have those spacers to fit different scopes but the spacers currently installed should be for your Swaro.

The Buehler line was purchased by Weatherby years ago and I believe they are no longer available.

No idea on why the keyhole but all the Weatherby's Mark IV's I've ever owned had a forearm pressure point, so that is not part of your problem. I tried free floating a Mark IV and it didn't improve accuracy at all - burning all that powder per shot makes for a hot barrel and after the 3rd to 5th shot in fairly rapid session you will start seeing a "pattern" as opposed to a group.

You can also shim the rear base if needed.