Fuel system troubleshooting

Hey everyone,

Looking for some suggestions rooting out a problem. 2004 4-cyl 2WD. About half the time I start it it runs pretty rough. Smooth as silk when idling or when I rev in neutral but when I accelerate or put load on the engine it sputters, not like it's trying to die but just momentary losses in power. At the times when it does show symptoms, if I keep driving they eventually fade away and it goes back to normal after about 30 mins of slow freeway cruising.

Also, over the last year or two I have noticed that with a very large load on the engine (accelerating above 70mph, steep hill, over-drive off) the engine would skip like this maybe once or twice. Replaced plugs a few months ago cause one lost spark (gap eroded away to nothing) and had hoped it would solve the large load issue but no dice. This trouble now feels like a much worse version of the same thing.

First thoughts were fuel system or electrical, leaned towards fuel because of the long-term gradual showing of slight symptoms over a year or more.

Replaced the fuel filter, didn't help. Pump was my 2nd guess, so checked the fuel pressure. 46 psi at idle and FSM says spec is 31-37.

The FSM also says I should have 38-44 psi when the ignition is ON but engine not running and I don't read any pressure then.

Its also supposed to hold 21 psi for at least 5 mins after turning off the engine but my pressure drops to zero within 10-20 secs.

With such high pressure I'm wondering about the fuel pressure regulator? Any tips on ways to narrow in on it and isolate whether that could be the issue?

Thanks in advance for any help.