You can use whatever microcontroller and only 1 would be needed. You can interface with a Real Time Clock (RTC) chip for time, and if you set it once, you could sync it up with any datalogs you might make as well.
Using RF range won't be all that accurate with a single receiver, and I've found that too many things effect range for it to be usefull as a good measure of distance. Maybe a directional antenna or something would work, but I'm not good with RF and I've found antenna tuning and general RF to be pretty complex if you want to do it right.
I'm not good at RF all together, but the idea I outlined above should be the best RF solution. No matter which side of the track you are on, as you get closer the receiver the signal will strengthen, until you pass the receiver. As soon as you pass the receiver the signal will weaken. If you can log the signal strength, whenever the strongest signal was recorded on the pass by will be the time you passed the receiver.
This should be equally accurate if you pass the receiver on the inside or outside of the track.
Of course, I'd like to see a none RF solution if possible. Like I said, RF has not been kind to me.