How to align Apple Music library with local library?

I thought maybe Apple Music might solve a problem. The problem is that I have built a huge music library over the years using iTunes and syncing to an upgrade iPod Classic with 512 gb of SD memory. Unfortunately, iPod Classics are incompatible with most car stereos these days. I have Apple Music through Verizon. I had heard about the issues with libraries getting screwed up 6 or 7 years ago, so I created a separate account from the one I used for my iPods and copied the same library to my laptop, then started using Apple Music. Playlist are there, everything seems good. Then I start looking at albums from some of my favorite artists, and EVERYTHING is messed up. For instance, with the Grateful Dead, Live Dead tracks appear on the streaming app on my phone under Aoxomoxoa, tracks get folded into different albums, album art is wrong, etc. Same thing when I look at Widespread Panic. Dixie Chicks last live album is somewhere random, not under Dixie Chicks, although it's in the local library.

Is there any way to get the phone streaming library to look like the local library? I'd like Apple Music to be something I can use, but if the albums can't be found, I don't see how.

[Re-Titled by Moderator]