That vacuum port opens into this bathtub shaped cavity in the baseplate. The round hole between my finger and the screw is the vacuum source for the power valve. There are channels connecting the vacuum port and the power valve hole to both primary throttle bores.
It's possible that a blown power valve could leak there. It could also be a cracked main body or metering block. Hopefully it is as simple as a gasket failure.
That would be one explanation for why you achieved best idle with the adjusting screws all the way in (out richens the idle).
My guess is that fuel is leaking into that area, where it is remaining in liquid form, after the engine has stopped running.
After it sits for a while, is the primary float bowl empty?