86 Pontiac Parisienne stalling

86 Parisienne, 120K mi, 307 8cyl. When the car is cold, it starts and runs fine. After about 15 min, especially once I get it up to highway speeds, it begins to hesitate, then starts to cut out. If I take my foot off the gas, it will idle fine, but when I reapply the gas, it cuts out. I can milk it along for a while like this, but it eventually dies completely. The problem is much worse when climbing hills; once the car starts hesitating, even the slightest grades will make it want to stall. Once it's dead, if I sit for a few minutes, it will start and run fine for about 5 minutes. The longer I sit before starting again allows me to go further before it stalls. If I happen to stall on a steep hill, it is much more difficult to get it started again. There is a strong gas smell when the the engine stalls.
The exhaust system is new. I checked the distributor cap and rotor, and coil, and they are good. New sparks and wires. New fuel pump. New air and fuel filters. EGR diaphragm was leaking, so I disconnected the vacuum line and plugged it. New 02 sensor and computer. New PCV valve and breather, though there is not much vacuum at the breather.