I think you are getting closer to solving it. Like Neil, I suspect the ignition switch. Your symptoms in the parking lot indicate that. The last two things you touched were the ignition switch (off a couple of seconds and back on) and the starter switch. If it was my car I would hot wire it to test the theory. I would run an extra wire from the hot side of the coil to the passenger compartment. Run a wire from the hot side of the battery to the passenger compartment. Connect both wires to a toggle switch, the kind that is either OFF or ON, not a momentary push button kind. Available from a hardware store. Put it within reach while you are driving. Heck, just tape it to the dash or something. Next time it dies on the road turn the switch on and see if you get your spark back. You can test the switch at home by turning the switch on and pushing the starter button. The engine should start.
WOW, NOTE: Don't forget to turn you toggle switch OFF before you leave the car. You don't want to drain the battery.