[Hotfingrs]

Sounds to me like you're perculating the fuel out of the carb. When you shut the engine off, the heat radiated from the engine and headers makes under hood temp raise to the point where the gas in the fuel bowls boils and evaporates or drips into the engine. When you start the car, there is enough gas in the intake, to make it run, but your fuel bowls are empty. Best bet is find a way to get rid of underhood temps, and isolate the carb, with a phenolic spacer.