I think you guys have missed the boat on this one.
Back to reality.
How about a link to the event rules.
Someone makes rubber strips to go around the o.d. of the wheels so they get traction. Or kart tires seem to be about the right dia. - big investment though.
You may want to consider a heat sink of some sort for the motors you choose. Or at least some way to get airflow past them.
Don