Hope I didn't miss something in the thread. A suggestion that may be too easy or too complicated, depending on how you look at it...
What about having an official time clock out of T&S from which all workers are tied to? The idea is to have the worker @ finish not only record run times, but the time the run finished on the clock as well. Or, maybe have a grid worker (additional?) at the entry of grid record the times that cars re-enter grid.