I'm sticking it out with IE after what I discovered about the current state of FireFox security. Unfortunately, in SP2, it seems as though the cache bugs are still there.
So I've started using CacheSentry, a free program for monitoring and cleaning up your cache. And I think I'll be sticking with the free version: the (proposed) UI for CacheSentry Pro is close on the verge of a submission to The Daily WTF or This Is Broken.
Slight disadvantages are that CacheSentry's limit for cache size is 700MB, and IE doesn't behave quite right when it hits CacheSentry's limit - I started getting stylesheet-missing problems again. However, dropping the limit to 500MB then expanding it again seems to have worked for the moment.