A worn float valve, or something holding it open, would be my first guess. Also, it's not unknown for floats to puncture and cease to float, which gives the same symptoms. The test with the old alloy floats was to take them off and shake them, listening for any fuel inside sloshing around. I don't know if the more modern nylon floats are prone to this. But a float that isn't floating (or where the float height is set too high) would have the effect of flooding the float chamber any time the fuel tap was on. (Or, if the problem is a sticky float valve, any time it feels like it.)
I think a complete dismantle and inspection, and a clean with an airline, is called for.