I went through controller setup again. This time I made the XBox button my Hotkey. Now I can start games by pressing Start and Right Trigger and I can exit a game to the main menu by pressing XBox button and Start. The Start button by itself, however, does nothing.
I should mention that the Start button works by itself flawlessly as you would expect from within Emulation Station to bring up the main menu. It's only within the actual games themselves that I have to use the weird Start/Right Trigger combination.
Any ideas?