Since it has to sit for awhile before it restarts, I would say you have some junk in you fuel tank and after it sits for awhile the junk floats up.
I would start with the easy things, before cleaning the tank out. Put a voltmeter at the fuel solenoid and make sure you are not losing power there. Open the fuel cap to make sure you do not have a vacuum issue, the vent behind the tank could be plugged up. Make sure the air filter(s) are clean.
Replace the fuel filter, fill the filter before you put it on and have a full tank. Doing these 2 things I have never had to bleed my tractor after changing the fuel filter. We have the same engine and fuel system.
I have included a diagram of the starting system should you need it.
Look at selectmanuals.com for a tech manual.
