The hard starting is a clue...a big one. Does it crank faster after it sits for a few minutes? When it does...does it just shut down like you turned the key off or just lose power and finally quit. I'm suspecting something might be binding up as soon as you start creating some good heat. My 2 stroke jet ski did the same thing when piston to cylinder clearance was right...piston would get hot, expand and stop the motor in it's tracks....wouldn't crank right away. After 20 seconds, it would crank slow. after a minute, it would lite right up and run great till I got it hot again. Do you have an oil temp gauge?
I'd go test it again and bring a ratchet and socket for the crank bolt with you....duplicate the problem and immediately after it quits, unplug the coil and try to crank it (timing error)...if still tough to crank, try to turn the engine by hand with the crank bolt. You need to determine whether you have a binding issue or whether you have a starter issue. I might also consider disconnecting the pump, pulling the bowl and seeing how that thrust bearing feels. also, make sure the impeller isn't running into the wear right or suction housing.