So the way we make this work is we create a link from the internal music storage folder to one on the external SD.
Some root browsers/explorers call this a "shortcut" but I use Root Explorer v3, which in my opinion is much easier.
You must have root to do this.
First, use Root Explorer to go into your external SD and create a folder, you can call it whatever you like. I used "GoogleMusic"
Next, create a folder underneath it called "files" and then long-press on it and choose the option to "link to this folder"
Next, browse to the Google Music internal storage directory (/data/data/com.google.android.music/files) and delete it (you may want to move the files to your new "files" directory first)
Then, click on the "create link" button to link to the files directory on your external SD.
Works like a charm for me.
Keep in mind these MP3s will be stored using Google's numeric naming convention, so they will really only be useful for Google Music. If you want to use the files for other players you can remove the .nomedia file from the directory with the MP3s in it.
Most of my info cam from a good write-up here on how to do it on an S3 running CM10: