Some followups here from the OP…
(1) Great suggestion from @fogcitynative to set up Shortcuts. I’ve got a small enough number of playlists that I frequently want to shuffle through that it’s no problem to set up a shortcut for each of them. That gets Siri out of the business of trying to control the music app and just lets the shortcut do the work.
(2) Many thanks to @nigel for the magic incantation of “from my music”. That’s making a big difference. I hadn’t stumbled across that before; I kept focusing on the term “library” because that’s how it’s labeled in iTunes and in the Music app.
(3) Regarding the suggestion from @jzw – I believe the “Show Apple Music” setting is only available if you don’t actually have an Apple Music subscription. (I remember turning that off back in the day.) I can understand that once you’re paying for Apple Music, hiding it would be hiding access to something you’ve specifically chosen to pay for, which would be a bit strange (Apple One bundling aside).
(4) I intend to update my original message and send to Tim Cook’s address–thanks for the encouragement.
This has been really helpful, and is a great example of how TidBITS Talk is a benefit to the Apple community.