Entering Time Machine has Black Box taking up screen space

A long-standing problem with Time Machine; as far back as I can remember.

If you have multiple monitors, and have "Displays have Separate Spaces" checked under Mission Control (System Preferences), you'll get this box when you try to use Time Machine. If you uncheck and restart (i.e., "Displays have Separate Spaces" is unchecked), Time Machine displays regularly.

This is fine, but you lose the ability of Separate Spaces -- specifically for me, this means I cannot do Full Screen Mode for Movies, videos, etc., as selecting Full Screen blacks out both the main and auxiliary screen for the video playing. Checking "Displays have Separate Spaces" solves this problem, and allows me to view a video in full screen on one display while having other apps working on the other display.

Given that it's been like this for as far back as I can remember (at least a decade) and I've reported it with every system, it appears it's not an issue worth Apple's time. I love Time Machine but this makes it unusable in my environment. I have a separate program which I use to clone my drive several times daily, so Time Machine is sort of redundant, save for its "oops" factor (i.e., I changed something in a FileMaker database file (which doesn't allow for more than one undo; I accidentally deleted a folder of files and emptied the trash, etc.).

It's unlikely I'll completely give it the heave-ho, but I do wish Apple would fix this problem.