You're very welcome!
I wonder if your mechanic did the compression test?
I wasn't sure about it, but if the problem went away (even if it was only one time) then you're mechanic might be right about the check valve in the fuel pump, the fuel is draining back into the tank and the fuel lines have no pressure, that's why it takes some time to start the car. You might want to try it again just to see if it helps, along with the pressure test.
That fuel pump is pretty cheap for a complete assembly, when I replaced mine I pay around $60 just for a rebuild kit, not the entire assembly! But your 2000 year GT isn't listed though, I don't know if there will be any differences between years (??). Just for comparison purposes check the following link:
CLICK HERE
The GREAT thing about our GP's is how damn easy is to replace the fuel pump, you just remove the carpet in the trunk and work form the rear seat. There is an access cover right behind the access panel at the rear seat. You remove a few bolts, remove the plate and voila! You've reached the fuel pump!!! See? Piece of cake...
Oscar.