Well, I think it depends on what type of music we're dealing with (MP3, itunes, Youtube conversion, etc.)
When you go to Google Music (Google Play)on your laptop, click on the album, then click on the bottom right arrow which brings up a menu. Then select edit album info. From there, you can choose a file to place on your album.
In Album Art Grabber (on your tablet only, no laptop), after you download it from Playstore, click "open" and it takes you straight to your collection that doesn't have artwork. Just click on the album and it should say choose image from (Last FM, MusicBrainz or your SDCard). Hope this helps!
Last edit: Jamaicman, in settings, I do not have any options selected like you do (Autosave, etc.) I wonder if that is making a difference?