This is probably a silly suggestion, but:
Could you find a layout that's extremely basic/empty and build up from there?
If that didn't remove enough elements, it might be worth including a custom page layout, like
$PAGE->set_pagelayout("my-plugin-layout"), even though it should ignore your invalid layout and default to
base. You could then use the class for your plugin pages (
pagelayout-my-plugin-layout) then remove elements you don't want with CSS.
It's not really answering the question (I don't see a way to register a one-off layout either), but do you think it might work in your situation?