1999 Ford Taurus Act's like its out of Fuel after 30+ minut

The 1999 Taurus 135,000 miles acts like it's not getting any fuel.
It does it when it has been driven about 30+ Minutes.

If I pull over, it also has a very rough idle - bouncing on the verge of stalling.

If I step on the gas the tachometer drops RPM's. The car loses speeds and
continues to slow down. If I pull over and shut the car off, and turn it back on
it runs fine for a couple of minutes and it does the same thing. (The next morning or even after a cool down it is fine again)

Several times I've been on the highway - at 70mph, and I've had the vehicle act like
it's out of gas. If I push the acclerator peddle down more that it already is, it doesn't respond.

The car seems to be fine for MONTHS on end - but if I take it for a long drive, I'm
can almost guarantee it will exhibit the 'out of gas' symptoms. I have taken it to
the dealer, and they tested the fuel pump. They said that under heavy acceleration the
"fuel pump does not provided adequate pressure."

It does not appear to be related to the amount of gas I have in the tank, it will
do this at 3/4 of a tank, as well as 1/4 of tank.

I am not having any problems with the transmission or shifting.

Here is what I've done so far:

============================================
I had the EGR Valve replaced - no effect.
I had the fuel filter replaced - no effect.

Paid the dealer to tell me what's wrong: They want to replace fuel pump.

Since the fuel pump is in the tank - it's expensive to drop the tank, and replace. I am skeptical that
this will solve my problem since the fuel pump is a mechanical device and imersed in the gas, How can it
decide to suddenly act differently on a long drive? If the dealer says it doesn't have pressure under
'high acceleration'- I'm ok with that. This is my daily driver, not a race car.


Any ideas. I do like Ford, however, problems like these make it difficult.