I was able to fix this last night. I wasted a ton of time on it. It took hours to transfer my music back over, so I did NOT try to repeat the process a second time, to test the solution.
Similar issue - iTunes on my PC looks fine. No album art issues. When I copy albums from it to my phone, suddenly Regina Spektor album covers (and other people) where all over the place, where they shouldn't be - totally messing up the visual.
First thing I did (FAILED) was try going to Settings -> General ->iPhoneStorage -> Edit -> All Song -> Delete (yes, I'd had enough - wiped everything). I started the awful process of moving music back over from my PC. Instant failure!
Second thing I did (SUCCESS) was to repeat the same deletion process from step one, but this time I went into the Music App on my phone BEFORE I restarted the copy process. Even though, technically, I'd deleted everything out of there, there seemed to be the 'ghost' of albums that I guess I'd purchased from iTunes. I suspect they were placeholders from my purchases. They had not re-downloaded yet, because I'd not tried to play them, but they were still there. I clicked on each one (about 20 in my case) and said chose "Delete from Library". Once I REALLY had nothing showing listed on my Music App, I went through the hours of selecting hundreds albums I'd made from my personal CD collection and copied them back over (AGAIN). When I awoke this morning, all the albums had transferred. All the album art was correct.
Horrible bug. I wasted hours working around it. I sure as **** don't want to buy anything else, until I know I'll never have to go through this again...