I would seem to think you are having a starting circuit issue. Next time it acts up check and see if positive and negative battery cables are/ get very warm to the touch, you may very well have corrosion and high resistance in the cables and the cables act up when they get warm cause the starter motor to lug down on restart. I would ensure the cables are clean and tight and perform a voltage drop test on the battery cables.
To check fuel pressure you need a fuel pressure tester and plumb into the pressure hose of the f.i. system. Some motors have a schrader valve which makes checking the psi very easy. I don't know pressure specs at the moment.
I don't think its a timing issue as that would cause issue on a cold and warm motor, however its always a good idea to check and ensure all the basics are covered.
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