1969 Carter AVS

The stock AVS carb on my 340 is flooding out. I had it rebuilt by a friend who is a retired race engine builder, and former NASCAS crew chief. I trust his work, but.....
Anyway, the car starts fine and runs smooth for a few seconds. Then, it starts to stumble like it has a HUGE cam installed. I can easily keep it running if I keep my foot on the pedal, but after shut down, gas pools in the secondary venturies.
I pulled the top of the carb off, and found the drivers side float stuck CLOSED. I freed it up, and it seemed to be better. Fast forward a few days, and here I am on Sunday am chasing the same trouble.

The car is stone stock, with a replacement mechanical fuel pump, and no mods at all.

ANY ideas at all? Anything I can check based on your own experience?
I am about to throw in the towel.

George