I solved the problem of why Assassin's patch wasn't working in Headerizer. It probably should be considered a bug in Headerizer. It can't stand it if the extension is in CAPS.
As for the other issue, I've begun to think it is NOT an issue if my theory is right. I've started to believe that I've been bizarrely using the wrong patch for years. It's actually an anti-patch. Yes, that's embarrassing. Just need to confirm it now. One moment.
EDIT: Nope. That wasn't it. It's still a problem, I guess.
Kaettekita edit: WAIT. I might have it now. I don't know why it would happen, but my patcher (which I've had trouble with before) could be making a patch that writes to that byte. I know that doesn't seem to make any sense, but none of this does. I'll test that.
Final Cutter edit: Amazingly and against sense, that WORKED.
It wasn't really my patching program, per se. It patched exactly as it was supposed to. The problem was: My patch was written by Lunar IPS (because I was making a non-header version) years ago. My current patching program (flips) makes the exact same error Lunar IPS did years ago. Maybe it goes to show how insecure IPS patches can be.

It would sound like a clear case for switching to BPS if that format was friendly to patch stacking... Anyway, Headerizer has solved the problem. Now I worry about other patches I have, though. How many were thrown off by whatever strange algorithm these IPS makers do?