Need some help here...

Lately when I try to start the engine when it's cold (sitting for at least a few hours), it doesn't want to start. I can usually get it to start by pumping the gas pedal as I am starting it, and I will have to give it a little bit of gas for a few minutes or it will die/stall at idle. Once it's warmed up then it seems to be fine.

First I thought it was the battery. But I got it checked at NAPA and it is fine.
I've tried the "poor man's prime" and it doesn't really alleviate the problem.
I also hooked a fuel pressure gauge to test valve on the fuel rail. It was operating at around 46 psi which are in the normal limits and after I shut the engine off it would slowly drop, but only to about 40 psi after 5 minutes. I'm leaning towards the check valve but honestly it is only a guess because I thought the priming technique would work better if this is the case.

What should I do? I'd rather not drop the tank and spend $200 on a new fuel pump assembly if it won't fix the problem.