I have the exact same problem as you. I have a 2001 model. Did the fuel
filter change do the trick?

I haven't tried a pressure gauge yet, since I have no way of reading it
when the problem happens (only when driving), so I didn't see much point
unless the pressure is consistently low (which doesn't make sense
because when it's not bucking, it can be driven hard without problems).

I DID have the filter replaced.  I went to jiffy lube because I couldn't
get enough clearance to do it myself.  I supplied my own filter and had
it fitted for $35.  The mech showed me the old one, and poured out BLACK
gasoline, it was really horrible looking so certainly needed replacing.

Have you tried to buy a $15 fuel pressure gauge and actually check your fuel
pressure

Did you replace the filter ????
(didn't read the follow-ups for a while)

Still no closer to fixing this yet.  I don't have the money right now to
let the dealer diagnose it.

Ruled out the power to the fuel pump (and therefore the impact switch
thing), by monitoring the voltage to the pump.  I was getting a pretty
steady 13.8v and it didn't fluctuate at all when hesitating.

I have also ruled out the IAC, since I tried it with the IAC unplugged
and still had the intermittent hesitation.

It's not easy to drive without the IAC, so I ended up letting the revs
drop too far and stalling it which threw a code.  Gonna have to go to
autozone and borrow their reader again to erase it.

I have a 98 Windstar 3.0 with 128k miles on it, and over the past few
months it has had a problem with hesitation and bucking.  The problem is
intermittent.

My mechanic has diagnosed a few things so far and a lot of money has
been spent on 'repairs' but nothing he suggests fixes the problem.  I've
now taken it back from my mechanic and his "shotgunning" repair
technique in order to try and diagnose the problem myself.

So far I've replaced the Throttle Position Sensor and the Camshaft
Position Sensor, and while that seemed to fix it for a day or two, the
problem came back.  (It's intermittent nature means it can run fine for
days).

There seems to be no rhyme or reason to the hesitation, it can happen
when you're pulling away gently, or when you're cruising at highway
speeds, or during a shift, pretty much any time.  Turning overdrive off,
or keeping the transmission in 1st or 2nd makes no difference.  Also you
can drive it really hard sometimes without the problem manifesting at
all.  Often I'll drive it hard 10 miles to work and it's fine, then it
will act up on the way home with about 3 miles to go.

As good as I can tell it feels like the engine is cutting power to the
injectors or plugs all at the same time.  And the loss of power can last
from a fraction of a second to a whole second before it recovers.
Sometimes you just feel a bit of spluttering as though only a single
injector or plug isn't firing.  I thought it might be a transmission
problem, but I'd imagine that the revs would climb while the
transmission slips, and that's not happening.

I've also had poor idling on occasion, but it's very uncommon, so may
not be related.

Any ideas what to try next?