For anyone with the AT&T Galaxy S3 (Model I747), I just want to let you know that the ROM I'm running on mine has native support for USB audio output and works with my FiiO E07K. It's called RootBox and you can get it here:
http://forum.xda-developers.com/showthread.php?t=2083922
However, the USB audio support is a bit sketchy and there's a special procedure you have to follow to get the phone to properly redirect audio to USB. If you don't do it this way the phone will freeze and you will have to hard reboot.
1. Open your music player on the phone and pick a song you want to listen to.
2. Start playing the song with the audio being directed through the phone speaker (It can be muted; doesn't matter).
3. While the audio is playing connect your USB DAC.
4. The audio should pause on connection and reroute to the DAC.
5. Press play and enjoy!
I hope this helps anyone who is struggling to find a ROM for the AT&T S3 that supports USB DACs.