Mike,
I've been halfway following this. Got two questions that may, or may not, be relevent!
Can you determine where the fuel is coming from, Seeping out the gasket between the airhorn and body would/ could indicate boiling, a leaking needle, or float level too high.
Second, try covering the front of the carb while it's running, to see if the air from the fan is evaporating the fuel while it's running. Maybe the same condition exists off or running, but the airflow dries it before it becomes noticeable. 
Third (I know I said two, but I just thought of this) are you sure the fuel lines aren't leaking at the carb. This happens a lot, but you might only notice it until the residual pressure drops. Last, shut it off hot and watch the inside of the carb to see what or where it drips.
Frank/Rebop
Bristol, In ( by Elkhart) 
