Last night I installed iSyncr on my GSIII (US Cellular), and the desktop version 3.6 for my Macbook Pro (running 10.6.8.) I had tried using Samsung Kies with no luck. In reading the install instructions for iSyncr I went back and installed and then with the Kies uninstaller, I uninstalled Kies properly.
It was then very easy to sync my iTunes music with my GSIII. I am using the stock music player to listen to music, and all is working very well. The iSyncr app was updated recently to fix issues with the GSIII.