The fault is not in the pump system, it is caused by pressure and temperature differences. As a motor cools, it does develop negative internal pressure, and could therefore pull fuel through the system.
Two of my friends used to run mod shifters at Grattan, but the flooding problems they had to deal with occurred just before races, while they waited in the grid line with full-to-the-top tanks. Having vents in the tanks did not seem to matter, the motors would flood like you describe. They had to use shutoffs in the lines as has been suggested.
One of them simply used a pinch clamp on the feed line between the tank and the pump. Seemed to work. There were a couple of drivers I saw who would leave the carburetors off of the motor until it was time to fire and warm up prior to the start of a race. I like the valve idea the best.