Underneath the accelerator pump nozzle at the carb barrels, is a small ball bearing used as a check valve, this sometimes sticks when the motor has sat for a period of time, if the ball is stuck it will not let the gas squirt into the carb.

Unless there is a cracked bowl in the carb, the gas can not leak down out of the bowls, as the jets operate by ventury (pressure drop caused by the air pulling through the carb), and the jets are channeled above the bowl. If the motor gets hot, it can evaporate the gas in the bowls, but they can not leak down unless the bowl is cracked. Seeing the glass filter draining back is not uncommon, however it is not the carb bowls siphoning, simply the carb's bowl vent allowing the gas to slowly bleed down to the pump after the motor shuts off. There should be enough fuel in the bowls (if adjusted correctly) to run the motor until the fuel pump picks up the fuel to the carb.

Normally with Edelbrock carbs if the fuel pressure is to high they leak fuel around the throttle base shafts and sometimes the top of the carb. A fuel pressure test is easy to do and will confirm the need for regulation. Keep in mind, a fuel pressure regulator is always a good idea and cheap insurance.

MHO, the accelerator pump circuit is not working properly, and you need a choke and a tune up.