Wait!! This is all backwards! The top FIRST people must know, weeks if not months in advance, what the game will be, so they would have an unfair advantage in designing the robot. That is to say, they couldn't help designing it before Kickoff.
The way to do it would be to have some teams design the game, then reveal it to the FIRST people, who can then build and compete against each other in the summer, with members of first-year teams (no longer rookies by this time) being the referees. We'd have to have some really picky robot inspectors, too.
It would be a sort of un-FIRST or anti-FIRST. In fact, we could call it LAST, which would stand for ______________ (fill in the blank).