Samsung Galaxy S III (S3) Won't Connect via USB with Android File Transfer with MacBook Pro - Mountain Lion

I saw some similar questions along these lines with newer Samsung devices, but I will post a question here anyway in case an answer for me ends up being an answer different than that for someone else. I have not seen a post concerning my particular phone, Mac hardware, and Mac OS.

Problem:

My Mountain Lion MacBook Pro (10.8.3) doesn't recognize my Samsung Galaxy S3 (4.1.1) for file transfer over USB. I am trying to use Android File Transfer, having been promised that it would solve all my woes.

The Situation:

I've downloaded Android File Transfer, and, when connected with my device, the app launches, but it just continues to demand that I attach the USB cable and or restart my device.

What I've tried doing:

Settings > Applications > Development > USB debugging

When set to on, nothing happens. When set to off, nothing happens either. I've turned it on, then on and off, then off, and restarted before, during, and after connection, and every combination possible. The result is the same: app launches and then gives error message.

USB Cable:

I've tried with two different new cables and the error message is the same.

Connected to a Windows device:

My phone is recognized just fine by my desktop PC running Windows 7. The phone is recognized and the SD card is recognized, and I can transfer files between them. However, my Windows device is not my primary computing device, and I am frequently away from home (otherwise, at this point, I would chuck the Mac and that would be that).

As with the person who posted a similar question about the Galaxy S2, please do not post answers suggesting the use of Kies, Bluetooth, Wireless, and the like unless they lead to me being able to use Android File Transfer via USB. I want my phone to work over USB and with AFT for a reason (speed, convenience, and better synchronization). Kies seems to be the default suggestion to solve this issue, but it is terribly buggy and it accomplishes file transfer much the same way that nuking my house would get rid of spiders. (Always good to have a little levity at this level of frustration.)