Well, I've tried using CE again, and this time I got it to work.
The problem was with read-only files.
Editing game settings (like starting event or starting map) with a read-only game executable made Cavestory display a weird error message, even with a clean copy of CS.
However, after getting rid of all the read-only attributes for the game files, I was able to edit with CE successfully on a clean copy of CS.
Apparently, I've never had the read-only problems with Sue's workshop, which is why I never bothered to check.
Thanks for bringing this to my attention though.