Well, this is less original than I thought...
Untill my sensors arrive, I've been working on software.
While wandering the web, I came across Andy Lippitt's page. His project is very similar to mine, with the exception that he is farther along with his than I am. His software and hardware are similar to mine to such a degree that I could almost just use his software without modification. As such, I am shamelessly using one of his ideas. :-)
One of the differences between his and mine is that he is currently switching to digital OpenServos. That's a great idea. I think I'll take it too :-). The OpenServo project sounds very cool. OpenServos would solve many of my problems, such as ground contact detection and determining actual servo position. It also fits in wonderfully with my other plans to set up my sensors with I2C.
Andy has created a very nice control that uses DirectX to render the Hexapod's current state. I have modified it enough to work with my software. It's a very nice control, and since I know nothing about DirectX, it has saved me tons of trouble. Thanks Andy!
Once my code has reached a more stable state, I will put it up so that others can benefit from it as I did from Andy's.