How to get Assistant to look for music only on my phone
Okay---Having wasted three full days of my life on this, and having finally found the answer, I will  post it in case anyone else encounters the same problem.

I installed a different music player, namely Pulsar, which I believe is designed to play only local music.  I also did a bunch of other stuff, like disabling YouTube and uninstalling Google Play Music, which might or might not have contributed to the solution.   But Pi Music Player is still installed and the voice commands still fail to control it properly.

I (once only) told Google Assistant to "play Steve Goodman on Pulsar", it did what I asked, and ever since, it's been defaulting to Pulsar for all of my music requests, just as I wanted it to.  Following the exact same strategy with Pi Music Player does not work.