Well, the competition was today. We had a pretty great two-phase design, but it wasn't working quite right today. The second phase wasn't giving us any additional pull. We ended up going 2.78 feet, which is better than a lot of teams whose cars didn't move at all. We ended up ranked #18 out of 70, but only the top 15 went into the second round. Our best run a few days ago was about twice that, which would've got us into the second round, but... oh well. Still, I think we're going to get a pretty good grade on the project, and we had fun, so it's all good.
I think we got video of the competition, but it doesn't show off how awesome our car is, nor does it explain how it works. So I'll try and shoot another video in a couple days to show everybody, once I get the car back from one of my teammates on Tuesday.
So thank you, everybody who contributed to this thread! Your ideas are all very much appreciated and helped a lot.