As you stated about the only way it could dribble fuel while not running is it's building pressure on the secondary bowl. Are you sure the bowl vent is cleared. I know if you leave anything with a hole open around here you will end up with dire dobbers filling the wholes. What about the check ball or rubber check located in the bottom of the bowl, assuming it's built like a holley, are they ok. I have seen some trash get into the ball seat or even seen a rusty ball, check, the rubber check can also crap out. I can't see it being anything else, wouldn't think you need another carb.