Hello
I have a 97 GT 3.8L GP with the exact same problem.. no fuel pressure when cold while cranking for several seconds, I cycle the key again.. and then I have good fuel pressure and it starts and runs great afterwards.. full power with no hesitation.. but when I let it sit overnight.. it hard starts again.. I agree that it seems like the fuel line empties or the fuel pump has an issue with priming, etc.

Did you ever find the problem? if so. what was the problem? Thanks