I went to Maker Faire this past weekend. Besides having an incredible time - I met Mitch the-TV-B-Gone guy and listened to talks by Massimo and Chris Anderson - I picked up a thumb joystick at the Maker Shop there. It's apparently from Sparkfun (COM-09426) and includes the breakout board. I'm in the process of figuring out how to add it to my LED matrix TicTacToe. The joystick has potentiometers for the X & Y directions, and like you suggested I could use the pushbutton for the Z-direction. But it looks like I'll still need another pushbutton or something to finish the move.
I've added the first part of the build process (Creating the 4x4x4 LED matrix) to my blog at http://www.whatmatters2me.com/?p=269. Check it out.