Update: I started a new Xbox 360 project - the default startup project that just clears the screen to CornflowerBlue. I deployed this app to my Xbox and tried to run from the NXE interface. It hung my Xbox the first time I tried to run it. In my mind, this pretty much confirms that this problem is on the NXE launching side.
Note that I have never had this problem when launching from XNA Game Studio Connect. That could just be a coincidence though. In other words, I cannot debug the problem because it only happens when I launch from the NXE interface (without starting XNA Game Studio Connect). I.e., the interface where you click on the game name and it takes you to the following three options: Play Game, Play Trial Game, and Delete Game.
Further update: I rebooted my Xbox 360 and tried to reproduce the issue again with the default CornflowerBlue app. It took me about 20 tries, flipping between Play Game and Play Trial Game before I got my Xbox to hang.