Latest Google Music update enables external SD card storage
External SD card storage is now supported for the Galaxy Note 3!
Here is what the Play store change log says:
(Dec 5th) v5.3.1316M * SD card support for offline music on KitKat (Experimental support on some older devices)
Yes it says that the SD card support is intended primarily for KitKat, but I am running stock JB 4.3 on a Tmobile SM-900T and it has worked flawlessly for me.
Granted my house is practically in the shadow of an LTE tower and I usually get 30mbps+, but I also travel quite a bit. It's pretty cool knowing I can listen to most of my music collection even when I have low or no bars.
The "experimental support for older devices" (lol) will probably work on other carriers and custom roms for the gnote3, too. Post the results and details of your setup after you've given it a try.
Sent from my SM-N900T using xda app-developers app