Back to the main thrust of my original post, I've just gone through and done a rough sort, putting creators, works and work-like pages into Category:Theatre, and all tropes and trope-like pages into Category:Theater. The only one I'm not really sure about is Turn of the Millennium/Theatre -- while the parent page is a trope, this specific page is a list of works from the era in question, so for the moment I've left it with the other works in Theatre.
The next step is renaming the categories to be a bit more distinctive from each other. I'm proposing renaming Theater to Theater Tropes, and Theatre to Theatrical Productions as noted above. Given how many creators are tagged with Theatre right now, I would also like to propose a new Category, to be called Playwrights or something similar (suggestions are welcome), which will become their new home, to keep them separate from productions.
Finally, we need to standardize on one spelling of Theater/Theatre for use as the media type. We have both scattered at random through both work names and subpages for tropes. Unless someone has strong feelings otherwise, I'm going to use "Theater".
Comments, suggestions, brickbats?
EDIT: And I've just discovered we already have a both a Theatrical Productions page and a Theatrical Productions category. Geeze, this is a mess.