2003 Chrysler Town and Country Engine Stalls, but only cold

My van recently began stalling. Mechanic found no codes. Fuel pressure was lower than design pressure but not drastically low. I think it was about 80% of normal. So he recommended replacing the pump to see if that would take care of it, but he had his doubts that it was the real problem. Since it is an expensive repair, I'd rather not do it if it's not the problem.

What else could it be? One thing that makes me doubt the pump is the problem is that the car idles fine and also stops stalling once the car has run for a few minutes. I can start the car and it will idle fine as long as I want. Only when I put it in gear AND give it that first bit of throttle will it stall. From idle in park, if I put it in gear but keep the brake on and give it no throttle it doesn't stall. Once I give it some throttle it stalls, but only if low throttle. If I put it in gear and immediately give it a decent amount of throttle it can go right through the hesitation which is barely perceptible in that case. And after only a couple minutes of running it will no longer stall regardless of throttle level. So even at very low throttle it will not stall once it has run for a few minutes.

Finally, does the 80% output of the fuel pump necessarily mean that the pump is dying, or is it possible the pump will operate fine at 80% for a long time.