I was looking in this and came up with a few thoughts:
The key to victory will being making this thing insanely light. I'm talking as light as function will allow. No paint, no stickers(except for flame sticks.. they are cool.), minimal wheel rubber(enough to make 1.5 runs or so), etc etc. Once you make a suffiently light robot you have a myriad of options on how to remove him from the pit.
As Admin said jumping is a good idea. As for how to jump I got a few ideas. You could try to make a solenoid work.. with suffient force it might be able to jump you up.. but you'd have issues of timing to get all 4 corners to move at once and such. What you might want to do is drive the robot up the plywood wall(more grip) and then use a solenoid to kind of shove it over.
The big problem with the jumping design is its dynamic.. if its off balance you might screw yourself. Also, its going to be heavy.
If I were doing it I would "cheat" and just use insanely sticky tires. Or even suction cup tires on the acrylic walls(I assume thats why they put those there).