What if we use John's suggestion and add a few minutes to a player's side when he/she reaches the hill? A simple extra button could do that. This way the climax of the match is given extra time.
A portable version could be made that utilizes a pair of wireless pads (one placed on each player's seat), and a large free-standing digital clock that has 2 time readouts.
I called a friend who works for an electronics manufacturing company, and he's already looking into building a prototype for me. He can design the software and hardware personally, including custom plastic molds and digital displays. The specifics of how it works can be modified as he goes along, so we can continue to sort out the details over time.