ThemeKey rule; how to target IMCE pages
As is my nature, I was totally overthinking this. Here's what I had to do in ThemeKey:

First, for the File field:

drupal:path = imce-filefield/%


Basically, this is matching the first section of the URL path with imce-filefield and then whatever else comes after it is matched with /%. 

This solves the problem for file/image uploads. The IMCE file browser used in the WYSIWYG editor (in my case, CKEditor) has a different URL path, so its interface is still broken. That one is simply:

drupal:path = imce


So far so good...