As it turns out streaming music downloads are not the same as purchased music downloads. "Add to Library" works very well for the purchased/ripped from the CD music downloads but not for the streaming music downloads.But I have no experience with streaming music downloads though. What happens if you just try to rescan ("Add to Library") the music folder containing the .m4p files? Music.app has an option to only show duplicates if you need to clean up duplicates. I would have to reboot to check iTunes.
I knew from the outset that streaming music downloads are "too good to be true" and there will have to be a catch somewhere.