Your symptoms sound identical to my electronic ignition getting heat soaked and shutting down. I could restart after about 10-15 minutes, but it was likely to happen again within a few miles. And this happened to me when I drove down to LA for the Pantera Palooza a couple years ago, driving on busy congested LA freeways and city streets on a 90-degree day. Not fun! So I totally understand what you're feeling! Except I also had my wife in the car who was not a great sport about it all and only wanted to add to the stress.
Anyway, I found that if I did NOT use the AC, it was less susceptible to heat soaking the ignition. But as soon as I turned on the AC, I was guaranteed it would die within a couple miles. Also, you mentioned you have fuel injection. Vapor lock is almost non-existent with a fuel injected car because the fuel lines are substantially pressurized. I would definitely try swapping your ignition box.