Just wanted to update that I seem to have things working.
While I was on the phone with apple yesterday I cam across this post: Re: iCloud Music 4010 Error
There the person mentions getting rid of tracks purchased on his wife's account. I realized I had 5 or 6 tracks that I had in my collection that were from my wife's iTunes account. While I was trying again to enable iCloud music library again I found those tracks and deleted them. This time everything worked! I can even sign in and out again and everything continues to work! As an experiment I even re-dowloade those few tracks (via family sharing) and things continue to work, so it's possible that for some reason it just didn't like those particular copies of those files (and honestly I can't remember if I had added them to my library via family sharing the first time or if we had just imported them a long time ago).
It's also possible this was just a coincidence, and it just happened to work this time. It's also possible Apple did something behind the scenes. At the conclusion of my call (while the attempt to enable iCloud Library was still running) the person I spoke with said that my case was going to be referred to the engineering departement, and he would call me back on Monday with what they found out (if anything). It's possible that maybe it was sent over there, an engineer saw what was wrong with my account right away and just fixed something? Who knows. But everything is working now, so I'm pretty happy.
The only hitch was that I ended up with a few hundred duplicate tracks (mostly as cloud tracks). But I was able to use View > Show Duplicates to weed those out pretty quickly so that's no big deal.
I will also say that I was a little nervous at the end of my call. The "Senior Support" guy who I spoke with at the end seemed a bit confused and seemed to think that you aren't supposed to be able to have both Apple Music and iTunes Match (and thought that might be the source of the problem), which I'm certain is incorrect. I told him that it had been working fine for me for the first few days, and that I had read many reviews of Apple Music where they explicitly talk about running both at the same time and why you might want to do that, but he still seemed to think you shouldn't be able to have both, though by the end he seemed a bit less sure about it and mentioned that he would be asking the engineers about that.
Anyway! I just wanted to update and give another datapoint and possible solution for some folks! Good luck! Let me know if you have any questions!
