Not quite sure physically how your gas is draining from your carb. Are you sure the motor is not doing an "after boil" or "heat soak" where the fuel is being vaporized out of your carb after it sits on a hot motor. The only way I can think that is possible to drain the carb after shut down is if the body of the carb is cracked.
Does this happen all the time, or just when its hot out and the engine is hot ?
And exactly what do you mean buy "priming" the carb, are you manually loading the carb's bowl with fuel prior to starting ?
Id find another carb, as a "shot gun" approach from your post, although your parameters are not to clear.
Also, what about an insulator between the carb and engine ?
You can "rebuild" that carb yourself, for a tiny fraction of what it would cost to have it done (not sure if in modern times a more simpler carb existed on a vehicle). Which would be a bonus, in the event the carb is "redone" and you find out that was not your problem. If you take it apart, be looking for a crack in the bowl. Ive never seen one, but from your description, thats where Id start looking, unless its dong an "after boil".
Check ebay and amazon for a refresh kit, if you dont have money to set on fire. Ive bought them for as little as $15 in the Motorcraft brand.