Unfortunately not on that first point, that's the first place I checked. It is set to "embed picture in the music file". As for auto-organization, I only have it set up to move the music files from my main SSD onto an external. Upon further inspection, it also has "also move remaining non-media files" unchecked. So neither of those are checked, although I completely forgot about auto-organize in the settings, so thanks for reminding me about that, haha.
However, the 'Set Retrieval Filter' button seemed promising, I unchecked all but embedded, and will see how that pans out.
EDIT: From further testing, it seems the retrieval filter was causing the cover.jpg to be pulled along with the files for some reason. I've now tried 4 albums with cover.jpg's in it, none have traveled with it. Thanks for all your help Bee-liever.