Thanks for the comments. This has gone from bad to worse. I've followed all of the steps, starting with resetting the phone and then with deleting the suggested files on the mac and reinstalling iTunes. Lastly, I completely erased the phone. Before and after I erased the phone, I got the same behavior from iTunes, it would recognize the phone briefly and start to sync and then suddenly the iPhone would just disappear from the iTunes screen. It did this as well on the restore side, recognizing the new phone, starting the restore from my backup and then failing.
One other point, I'm using a Seidio usb dock connected directly to my Mac, but I doubt that is the root of the problem, as iTunes stopped opening automatically when I used the original iPhone USB cable directly to the Mac as well.
Any other ideas how to get out of this purgatory?