Why not have a fail safe installed (and set up correctly) on the cars, then simply have the transmitters powered through an umbilical type cable from a power supply on your rostrum (no need for batteries), then make up a simple switch panel to turn transmitters off when you decide time is up. Car will drop in to fail safe..
The umbilical cables will double as security for your transmitters too..
Jamie's idea above for a simple mechanical timer switch could be incorporated in your switch panel if you so wished..
A simple push button timer switch like this may do..
http://www.free-instruction-manuals....f/p4786356.pdf