There is a simple solution to this entire mess: make each member of your team responsible for a single ball on the trip down to Atlanta. As an incentive, you could tell them that it is supposed to be their pillow.
This is our emergency plan in case we don't have enough room in the undercarriage of the bus. And it is this point wherein lies the flaw for your situation: I don't know if the airline would appreciate 20+ students armed with poofballs.
_Alex