Ok, so there are a few solutions for getting our libraries back to normal. But, we still can't add offline music if we disable iCloud Music.
So, here's what I'm doing: I'm leaving my iTunes music untouched (no iCloud), and I'm using iCloud on my phone. Ok, but that still leaves album and metadata issues.
I found that I can add the correct album to My Music (capitalized to mean Apple's service), and that seems to correct the issues with album art. And, seemingly awesome enough, it shows the songs as already existing on my device. At this time there are two albums, one from Apple Music and one, corrupted, from my collection. But if I delete the corrupted album, the downloaded songs from Apple Music's album disappear and must be made "available offline" IE must be downloaded.
Not an ideal solution, but it gets worse. Sometimes Apple Music doesn't have an album. Take, for example, music from the movie The Mexican by Alan Silvestri and Various Artists (Apple Music thinks this is the movie Mouse Hunt...). I can't add this to My Music, which means I have to be ok with the album being messed up or lose it completely. There is no way to override Apple Music's redefinition of this album as Mouse Hunt.
And if I choose to re-sync with my computer, I will lose every song I downloaded from Apple Music...
It's frustrating, and the only reason I'm still debating whether or not to continue with this service.