I'm just rewording this post to make things more clear.
HOWEVER, If I click edit and then Preview, or Fullscreen Edit, the quicktags work fine. If I exit Fullscreen Edit back to the default editor, the quicktags continue to work fine. If I save and then edit the page again, quicktags are once again broken unless I first preview or use fullscreen edit first.
I was using v2.2 when this began, cleared cache, upgraded to v2.3 and then v2.4 and did the upgrade stuff, cleared cache again, etc. I tried running a file check but it just drops to a blank screen after a while, and yes I changed php to a longer timeout.
I did make some configuration changes but none of them should have anything to do with this, and I've since gone through and reversed any changes I can recall and have been looking for others with no luck. I'm completely stumped.