Now I'm depressed.
I went to play music and it rebooted, and kept rebooting. Never stopped. This was running Steel Droid.
I did a wipe with CWM, flashed to factory 4.02, did a factory wipe, flashed to 4.04, did a factory wipe...
What it's doing with the factory images is it reaches the point where it asks to log in to your Google account, then reboots.