Hi friend, not sure if you've found a fix for this but I had the same problem and I managed to sort it out - I'll detail here just in case you or others are still struggling.
I did a number of things, not sure which one worked, but you could try all if you're having the same problem. Firstly, I updated my MacBook Pro, my iPhone and my Ultra 2 (all three had an update pending). I then set my Ultra 2 back to factor settings, i.e. disconnected it form my iPhone. Then I plugged my iPhone into my Mac, where all of my music is saved, I re-authorised it via the Music app (under Account) and synced/backed-up. Following that I set my Ultra 2 up as a new Watch and added the playlists that I wanted to add. Last time I did this, only the music purchased from Apple downloaded and not music I had installed from CD's. Initially it appeared to be doing the same, i.e. it appeared to only concentrate on music purchased from iTunes, however, after that it then started downloading the rest.
To be honest, I've only just done this today and I haven't checked if they actually play without my iPhone around, however, I'm no longer left with certain tracks greyed out as before so I think it's sorted (I've added three playlists so far). I'm going to test on a run tomorrow... if anything goes wrong I'll update this comment.
I guess there was a bug that's been ironed out by an update, or perhaps updating the watch to the latest software before setting it up as a new watch helped. It was a relief to me either way, as most of my music comes from CD's!