I figured it out! After turning AM off and on and getting less and less space back I finally went in with iexplorer and found all the garbage files that Apple music was storing. Inside the "media" folder was a folder called "cloudservices" (or something like that), and there were hundreds of MP4 files. I deleted all the files there, and boom, my 3.4 GB of free storage space reappeared, and when I opened AM again everything still worked perfectly. Mother-f'er.