Many years late, here's the completed project!
I started by using a laser cutter to engrave the ouija board. The letters are arranged on a slight curve so that the arm can sweep across them hitting all of them. (The planchette still needs to be able to move to hit everything, but I wanted to minimize that as much as possible to keep the motion smooth and natural.)
After that, it was a matter of attaching the arm and calibrating the letters. Each letter is stored internally as a combination of arm and planchette servo positions. I just did this by hand, tweaking positions until I got good alignment for each letter. I could probably have calculated them all based on the distance and angle of the arm and planchette, but I think that would have taken longer than just doing it manually. (To be really cool I'd have set multiple different position pairs for each letter and chosen from them at random to make the motion more natural-feeling, but I didn't have the patience.)
Once that was complete, it was ready for Halloween! I set the board up on a table in my yard and had friends tweet messages to it throughout the night. It was a big hit -- adults were delighted and children were startled :)