Alright, just a bit of clarification...
Bots vs. humans = BAD IDEA! This would be a team socialish competion, not an invitation for lawsuits
Game Length is restricted to exactly 2 minutes, in addition you'd add 2-3 minutes for set-up/clearence. With 3 teams on each alliance, at most regionals, with single elimination, an entire tournament can finish in under an hour. Which means that this would work very well as a lunchtime competition.
You could save the very final game for a timeout during finals or one of the "cool down" periods. The full set-up/playing time is < 5 minutes. The only problem I see with this is that the players who will likely represent their team in the dodgeball final might be instrumental to their teams, and would probibly be using that time to fix the robot, or prepare for the coming match. To fix this you'd make it clear that even though alliances are set in stone once chosen, team representitives are not. They can switch out players in between matches as much as they'd like, which should help alliviate that issue.
I'll be submitting a proposal to the ColoradoFIRST Regional in a few days. Wish me luck.
Meanwhile do any of you have any specific game related concerns or ideas?