Earlier today, I stumbled across the --platform option to pip install. I believe that's the major missing piece of the puzzle for me. Now, I know how to structure tests so as to be guaranteed to be able to install, or not able to install, a test wheel file.
It's going to be a bit more effort to make use of this, because I need to either wrap the low-level wheel-creation code that doesn't actually write a file, or I need to rename the output of the higher-level helpers. I hope the latter works, because that sounds like way less effort. (It... looks like it should? I'll need to test this some.)
Anyway, I don't want to work on this during the week any more, so I'm going to take things easy for the next two days, then start writing the tests.
I'm going to start on that break now, and try to relax before getting to bed.