My proposal:
Offer awards to the Quarter-finalists, Semi-finalists, Championship Finalist and Championship Winners. Thats a total of 24 awards (if no backups), better than the 30 as current (if no backups) - thus aiding FIRST in their "award problem". The division fields will be where the 1st, 2nd and quarterfinal rounds are played, with the 1st/8th seed playing on their "home court". Semifinal and Final rounds are played on Einstein as they are now.
Drive teams would be awarded with their finalist trophies after their match, either on the Field they play on, or onto the stage set up beside Einstein. This way, after the teams lose the event, their drive teams can be given that "lets give a hand to this great alliance."
The reason I would drop the whole "Division" thing, and settle for more "finalist" awards, is because divisions alter every year. The word can be used in another way for FIRST by dropping it from the current use. Divisional Finalists are nothing more than Championship Quarter-Finalists anyway. Rather than saying you are in the "Curie Division", you would say "Curie Field" or in this year's game: "Curie Court".