brivette, it's not possible to wire the beeper to all six LEDs, unless you buy six beepers!
I've been working on a circuit for this. I bought the kit recommended on the Instructable and no matter what piezo I hook up to it, it makes a "click" when the other LEDs light up, and then beeps when the last one does. The click is quiet but I can definitely hear it.
Then I did what I should have done to start with - I bought a Picaxe 14M2 microcontroller and just the other day finished the code so that you can change both the pattern of the beeps, but also if the beep happens on every LED lighting up, or only the last one. So, four patterns:
Circle of LEDs, one at a time, beep on every LED (like in the movie)
Circle of LEDs, one at a time, beep only on the last LED
Two half-circles of LEDs, beep on every blink (like in the Instructable)
Two half-circles of LEDs, beep only on the last LED
I added the two extra modes because having the actual piezo beep on every blink is kind of annoying. You can set the modes by flipping a couple of switches, which I plan on having on the underside so you can't see them when the mine is stuck on a wall (or your refrigerator).
I'm willing to share the code for this but have no interest in building any boards for anyone. This is a project for people with some experience programming microcontrollers and making a small breadboard for them.