Small Engines (Lawn Mowers, etc.): Engine dies when hot, electric fuel pump, gap access

Question
22hp Robin EH65 twin OHV (4 stroke/2 cyl) engine running a hydraulic pump for a small tractor

Symptoms
1. Engine will always start easily when cold and run smoothly at idle and under load - no problems
2. Engine will die after running for a while (hot). Very difficult (if not impossible) to start immediately after dying. The longer the wait, the easier the engine will start and the longer it will run until it shuts off again. Has the feeling of running out of fuel when it dies.
3. Battery is grounded to the engine which is directly mounted to the frame

Solutions
A. Initially suspected fuel flow problem (possibly vapor lock). Checked and changed fuel filter to a larger filter. No Go. Changed diaphragm type fuel pump to an electric fuel pump (2-4 psi) No Go. Now has good fuel flow. Carburetor has float bowl and fuel shut off solenoid. Float bowl seems to ok - no binding. Fuel solenoid seems to function ok. By the way, carburetor body is not hot when engine dies. Since engine runs ok during initial start up and under load, I assumed carburetor is not clogged in any way.

B. Ignition is flywheel magneto type. Suspected maybe flywheel expands when hot and possibly closes gap. Access is difficult but did our best to check magneto gap. Seems ok  @ 0.015" (spec at 0.012-0.020") Possible that magneto is weak to begin with and heat makes it even weaker? If so, wouldn't engine still run with one cylinder unless both are bad? If so, is there an accurate way to test magneto?

C. There is also a stop diode in the system. Even without the diode in the system (we isolated it) the problem still occurs.

At this point, I am stumped. Please help.

Answer
It's possible that you have an issue with the ignition module failing when hot.  You could check for spark when the engine dies....it should jump a 1/8" gap if the system is OK.  The diode is for the charging system and unrelated to the engine running.  A couple of things to suspect are the fuel tank vent and loss of compression (due to valves and tappet clearance).  You can loosen the fuel cap to see if the issue is related to tank venting.  As for compression, you would have to listen for a "whisping" sound in the exhaust if there is an issue with a burnt valve or improper tappet clearance.  Hope this helps.