I took the intake manifold (if you want to call it that) off and resealed the connection between the block and intake and between the carb and intake. I think I will order a new intake manifold, it being plastic, might have a hairline crack that I am not able to detect.

This is not an uncommon problem, the engine has overheated at some point With the seat pushed back into the bore, stake the rim of the bore at three points with a center punch. Then, using a pin punch, peen the aluminum around the circumference of the seat. Check the valve clearance, reassemble and you should be fine.

It does not sound like an electrically related problem to me either. Nor does it sound as though it improves "after cooling off". It improves after WAITING....but I don't think it is because of cooling off. OK, now answer this set of questions please. Does the machine have a fuel pump, or is the gas tank mounted higher than the carburetor? How many hours of operation would you guess the engine has accumulated? Have you recently changed the fuel filter or fuel hoses? The situation you describe, now sounds very much like what happens when a machine utilizes a gravity fed carburetor......and something is causing the flow of fuel to the carb to be reduced to a small trickle, instead of the proper flow volume needed for sustained running. Picture this: The machine has sat there until you show up and first start it. The carburetor bowl is full of fuel because during the hours or days the machine sat, the small flow of fuel filled the bowl. Now, you start the engine. In 2 minutes or less, the engine will consume the gas in the bowl and the engine hiccups, coughs, and dies. You will have to wait long enough for the bowl to slowly refill before you will get 2 more minutes of run time. How long will the engine run just idling? At idle, it should run much longer because the fuel consumption rate is so much smaller than at high RPM. A badly clogged filter in a gravity fed system can cause this to happen. A carb needle valve that does not open far enough can also cause this. A sticking or rubbing float could cause the needle valve to stay nearly closed and that would cause this condition as well. A kinked or pinched fuel hose might also cause this.

****"I have an 18HP Briggs twin with same symptoms."*** How much "the same" is YOUR 18HP Briggs twin, to the example machine in the OP (who, by the way, has not bothered to reply yet)?? But to answer the portion of the question that COULD apply to ***"wouldn't a nonfunctioning float valve cause the flooding to happen at all times, including parked in the shed for days or weeks between uses?"*** Yes, it would "attempt to flood" at all times, BUT, if your engine is fed by a fuel pump (instead of gravity) the faulty float valve can still leak enough fuel to flood the engine and cause "hard starting hot", simply by the amount of fuel in the fuel hose between the output connector of the fuel pump and the carb float valve. If the engine were stone cold....that same amount of fuel leakage would not hamper the engine from starting up (could help actually as it would be a "rich mix", which a cold engine wants for starting). The fact that YOUR engine is hard to start after a hot shutdown could be due to flooding temporarily because of the scenario I described, but not filling the engine crankcase with raw gas during storage because your engine might be "pump fed". You did not state whether pump or gravity, so I can't say how exact your situation is to the OP's situation, and since that person has not yet divulged the same info.....it's anybody's guess whether the engine configurations are the same. Could be, but so far....no proof! The small amount of fuel leaking into the engine intake after shutting down a pump fed carb could certainly cause "hard start hot from flooding". BUT, that small amount of gas would evaporate and be gone long before it could make its way into the crankcase (the engine would still be somewhat warm when all the fuel finished leaking out of the carb and estabilshed a "stable level" in the bowl. Another thing I will toss in here, and forgive me if I seem to be making "an assumption". You are not by chance "using the choke" when you attempt to restart the engine hot, are you. Before you get all defensive, I have had a couple of cases where an owner/operator complained of "hard start hot" only to learn (by chance) that they were ALWAYS "pulling the choke" to start!!!!! HOT or COLD. Remember, hot engines flood at the slightest provocation, but cold engines "like" a shot of gas.