Ok, I am back.
After upgrading to iOS 8.1 yesterday, the music sync problem came back. So I once again tried the fix and it worked and has worked properly after several syncs since. Here it goes:
Launch iTunes (12.0.1). Store Menu > View Account > Enter PW > Manage Devices > Manage > Remove device
Exit and go back to iTunes and select the phone. Deselect sync music and run a sync. Quit iTunes when done.
On the phone: Settings >iTunes & App Store > Apple ID > Sign Out [turn the phone off and restart it] Come back to Settings > iTunes & App Store > Password > Sign In.
Connect the iPhone to iTunes. Select sync music as per your usual setup and music installed properly.
The next time this happens, I may try just signing out on the phone first, without the iTunes.
I am still noticing some weirdness, but syncs are working fine and my music, apps, photos etc. are properly working on the phone. But the phone is not showing on manage devices under my account information (weird), and on the phone the app store keeps showing apps available for update even though I have already downloaded and installed them 🙂 but still 😕