Apple Music removes songs from playlists--any better way to restore than my tedious fix?

So all my playlists disappeared when I migrated to a new computer (probably user error though I am suspicious), and I finally found out how to restore them, only to find that Apple Music is playing fast and loose with music that I purchased and that belongs to me. It deletes songs from the playlists saying "they can't be found" in the weird online matching system that icloud/Apple Music use. In fact, they can be found in my library, but they are in protected status and I assume therefore get deleted from my newly restored playlists--it's just gone so you'll never know it was there unless you go back to each playlist and compare what you originally had and what Apple Music "allows" you to have. Here's the process I'm using, so if anyone has a better idea for this, let me know.

1. I reloaded a music library I had before I made the mistake of subscribing to Apple Music and icloud services. [Close Music, open it pressing "option" and choose an older backed up library] All my playlists are intact there, but none of the songs will play, saying they cannot be located.
2. Instead of trying to fix that, I decided to move all the old playlists to my new library. You do that by exporting each playlist [File/Library/Export playlist] to your desktop. Then close out that old library, open the new library [Again, by pressing "option" as you open Music], and import all the playlists [File/Library/Import playlist].  However, each one beeped as I imported it and said "some songs could not be found." When I opened the playlists, they are missing songs, some are totally empty.  This is apparently because Apple Music doesn't just leave your music in a file, it puts it on the cloud, deletes it and your metadata and matches the songs with ones they have in their library and when you want to play your song, it gives you the match it chose.  This is bad if you have a special version or live or whatever. But as far as I can tell, if some of the songs you had bought yourself and loaded on your computer are now considered "protected" in the match system, Apple will still let you play them but they get deleted from your playlists!  You can't even see that they were once in the playlist.
3. However, those songs actually still exist and are playable in the new library. So, if you go back and note all the songs in each playlist, search for them in your library, and then add to that playlist, they are all (so far) playable. But the level of effort to do that is seriously annoying.

If anyone has a better way to either import the playlists in a way that they don't delete protected songs (which I had purchased) or to use an old library that can't seem to locate songs, or some other way to solve this, I will be grateful. I have spent hours searching for "playlists missing songs" and "restore music library from time machine" and get a variety of guidance that doesn't seem to be this particular problem.

Thanks!