I switched to another phone as well and will be selling my AT&T GS3. In order to avoid having to do the Google Services Framework trick to force the update, I updated manually instead. It's a lot faster, too - took me less than 10 minutes.
OTA is WiFi. The problem is that, so far, it is not updating via OTA. I thought, perhaps, that if the sim card is not active, it would never update via OTA.
Been scouring the net for this answer with no luck so far. I have a razr maxx with 4.0.4 on it and I want to update and root this inactive phone before I transfer my service to it. Have not been able to update from 4.0.4 to 4.1.2 via wifi. I have no sim card or sd card in the unit. I was able to download the update, and was prompted to install it, but after a restart was given the "software failed to install" message. My goal is to remove bloatware and set a mile overclock on it in hopes I can continue to use my razr maxx accessories with a phone that is a bit faster, leaner and more realiable. Any tips on this would be greatly appreciated by this newby.