Marshall
I believe you are on the right track. The float valves or something in that fuel delivery circuit (dirt, rubber bits) that inhibits float valve operation is going to be your problem.
When the car is parked (ignition off), the only thing preventing fuel from from flowing into the carb (and beyond) is the float valve. If the float valve is defective or obstructed, then over time fuel can flow into and through the carb until the gas tank empties; just the same as if it were sitting there idling (for 3-6 months).
I've seen this happen. I don't think it was that uncommon, maybe isolated to the Chinese carbs. I know Kirk would send out a new carb just for the sake of a phone call. Personally, I have removed the air filter and have seen the carb full of gas, overflowing the top and onto the floor. Obviously fuel had already filled the manifold, cylinders, sump, etc.
Be sure to back-flush the fuel inlet port and jet with compressed air or carb spray before installing the new valve. Any fleck of dirt or rubber bits ('ethanol induced') that can wedge between the needle and seat will continue the same problem you are having. The fuel inlet circuit above the valve must be clean. When you blow it out, do it over a white rag to see if anything comes out. If you find black rubber bits, then you'll need to look upstream and replace whatever is deteriorating.
And: Before firing up, change the oil and rotate the engine a number of revolutions without spark plugs installed. You don't want gas in the crankcase oil, or try a compression stroke on a cylinder full of gas.
And: When you get the car home, disconnect the fuel line from the carb until you do your repairs. If you find that it drip, drip, drips when disconnected, then you know that drip, drip, drip can flow straight through a defective float valve.