I've got a real challenge for you guys!

[Cephas]

Oh, most definitely... bwahahahah!

If it's not the backflow valve on the pump, (which it might be)

then it sounds like your injectors have postnasal drip. The running roughly thing
after a hard start is one of the bigger indicators- you have a fuel- soaked cylinder or 3,
and it/they are taking a while to dry out.

my thought.
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This is exactly what was happening with my car. It got to the point where I could hear the injector spraying fuel after I shut the car off if I put my ear near it. Scary.

ELVA, since you say this happened on several sets of injectors, I think you have to start by checking fuel pressure once the car is off. It sounds like you need a new fuel pump (the check valve is leaking).

[ForcedFirebird]

Fuel leaking back is a simple diagnosis. Put a fuel pressure gauge in it, start the car, shut it off and the pressure should stay ~40-ish for a good amount of time after the car is turned off. Usually it's noticeable if the car is harder to start when it's been sitting vs recently driven.

Is it totally random, even of the car was turned off recently?

[ELVA164]

Fuel leaking back is a simple diagnosis. Put a fuel pressure gauge in it, start the car, shut it off and the pressure should stay ~40-ish for a good amount of time after the car is turned off. Usually it's noticeable if the car is harder to start when it's been sitting vs recently driven.

Is it totally random, even of the car was turned off recently?

Yeah, I can't see any pattern whatsoever. There may be one, but it's pretty sneaky if so. Alright, I'll read up on where to pop in the fuel pressure gauge.