LlamaNerds, the way to solve it is to create a new category with a new page, i.e. not a category you have previously used. In my case I created a category called "sandbox" and a page called "debug". So in the Add a New Page box you enter sandbox:debug. When the editor is displayed just add [[Module ManageSite]] to it and save. Then go to that new page and the working site manager will be there.
Then go to Themes. Select admin from the category list on the left. Then Choose a theme for that category like Clean for example. Make sure you un-check "inherit from _default". Then save changes.
As a precaution in case it happens again I have left the sandbox:debug category and page in place on the two wikis that were affected by this rather frustrating problem. Bu the solution does work.
I hope that helps.
Edit: I reproduced the problem again by setting both the default and admin themes back to Bloo to check that what I was saying above was correct. Like you I could tthen not see a list of Themes. But taking out the nav:top and nav:side navigation elements as you suggested did then make the list of themes re-appear, so it was possible then then to change the default and admin themes to something else.
It must be something buried deep in javascript that is causing all this.
Rob