Is the starter still working when you try and start it after?
If its not, the starting may be having a heat soak issues, where as the solenoid gets to hot and needs time to cool down.
Other than this initial point, it may be your fuel pump, as its tired.
As for driving hard, I wouldnt do so any more until you correct your problem.
check the PCU unit, its a known common problem with the Z's. Sounds like similar simptoms.. ( I know, changed mine! looking at about 300$ roughly)... Its found front of engine, passenger side/center, looks like a square chip... Hope its not that but sounds like it... do a search online for PCU 300zx and you'll get alot more info... :dunno:
On the drivers side on the timing cover there is an adjustable round timing plate, when I jiggle the connector on it, it cuts the engine off. I was checking the temperature of the PCU and i discovered that. I guess there was arcing when I was reving too high and it cut the engine. But why the delay to restart?
It is tough to test because you need a good stretch and hope that it does not die in a bad spot, also that it starts again after 10 minutes.