Carter AVS on a 340 drains of fuel

I have a 1969 Swinger with the original 340\4 spd that has been completely restored over the past 3 years. The carb is the original Carter AVS and has since been rebuilt 3 times by a "Professional" carb shop. Here is my problem, when I shutdown the engine, the fuel will siphone from the carb within an hour or two. I can't find any leaks, the fuel pump has been replaced, as has: the fuel tank, all fuel lines, filter, tank vent tube, sending unit in the tank. There is nothing left to replace other than the carb from what I can tell. I wanted to avoid that as it is an original numbers matching restoration.
Any suggestion? Thanks.