I had a few problems when I first set up Groove (When it was Xbox Music), I "Dumped" a couple of hundred albums on it and I didn't realise I had a circular reference on a PC that went to a network drive and it caused all sorts of problems as the software tried to sort it all out.
I have found Groove doesn't like large databases of local music presented in one go, it really doesn't like circular references.
So I started again but took the time to understand (Sort of) how it worked with local and music pass music, so I sorted out where each device looked for music locally, then added maybe 10 albums, got that lot working across all devices then added more, finally added in the Groove music pass stuff. Groove does try to match albums against it's own database and this can cause issues if it can't find a match (In it's opinion).
I now have 500 plus albums made up of a few I have purchased through the store, several more on OneDrive, but I have replaced most with music pass stuff (I still have my original MP3's just in case and only use OneDrive for albums I can't replicate with the pass for example King Crimson).
With about 7000 songs on 4 devices all downloaded to each for offline listening, the same number on each device, all the albums and artists pictures show up with one exception (Let it be naked doesn't show album art, the non naked version is fine). The whole lot replicates to my Xbox One as well (This is hooked up to my Hi-Fi).
What I found was particular albums for example "Quadrophenia" by the Who, the version I had was with several bonus tracks from the film so it counted as a Various Artists album rather than the Who's classic original release and caused it to split into two albums to boot. As I had the music pass I just deleted the "Wrong" one and download it from Groove and it sorted itself out.
I have had so few problems since I rebuilt it at the start, and when I have, I have found having the web login facility to act as my "Master" reference very handy.
By using the filters you can see what songs/albums haven't download on one device properly and sort it out easily and keep the thing sweet across each device.
For me it was well worth sorting it out and in some ways it's a bit like the way we used to sort out vinyl collections, constantly re-referencing the collection.
Not saying any of that is helping you, but to me Groove has been fantastic, I am listening to stuff I wouldn't have, finding old friends (Albums) that I had forgotten about and because it's all paid for with the music pass, new stuff I wouldn't have bought if I had to buy the CD.
If I was starting out with it now, I wouldn't use locally stored albums, I would put all my ripped CD's on OneDrive, get that lot sorted and then add the pass and as mentioned keeping an eye on the totals (Songs and albums via the web version) to make sure it's working properly.
EDIT: Because Groove tries to match it's database, you do see some albums where tracks aren't available to download because of copyright, if Groove thinks your album is one of those it could be that is why some tracks are missing, yet sitting right next to it in the Groove catalogue is a re-mastered copy where the tracks are available, maybe worth a look, and also check your settings on each device, this used to be more critical than now but still worth a look.