"I know I only think X because of bias Y, so my actual belief should be Z", you seem to already have solved the problem in that instance, by just switching them out (in lambda calculus: E[X:=Z]).

You'd think that should be the case, but beliefs don't actually work like that. You may believe that you believe Z, but you'll still behave as if you believe X. It's possible to override belief X, but it's not as easy as simply recognizing that you should override (or at least, that's the case in my experience. Yours may vary).