When driving off road or even over uneven paved roads, such as near a construction site where the road way is different heights, the truck really wants to pull every which direction over these spots. I have to fight it. Is this a worn steering damper/stabilizer? The truck has 203K, so it would be about time...

 

If it just pulls in whatever direction the road leans, or pulls back and forth over uneven road, that's not a stabilizer.

Sounds like something's loose or your alignment is off.

 

What could be loose?

 

Ball joints, tie-rod ends, pitman arm, wheel bearings, spring bushings, whatever

 

Could be not enough caster.
Has it been lifted?

 

It's not lifted, it is all stock. It just likes to go where the roads tells it to, not necessarily where I want it to.

 

Do the following first.

1.) Tighten the gearbox 1/4 turn or so. Take it for test drive and try another 1/4 turn adjustment. Rinse and repeat. If you feel high resistance while tightening the the adjustment bolt in the steering box you went too far and need to back off. If you over tighten the box you'll destroy it.
2.) Replace power steering fluid.

If you still are having issues.
1.) Check ball joints.
2.) Check drag link and tie rods.
3.) Check front bushings and the springs themselves.
4.) Check track bar bushings.
5.) Check wheel hub.
6.) Replace anything that looks worn out.
7.) Have an alignment done.

And finally
1.) Look at replacing the steering box.

 

What is the procedure to drain the power steering fluid out?

 

Below is a link for the PSD since it's different then the gas engines. The PSD has the HydroBoost which the gas engines don't need.

Ford Super Duty Power Steering Flush | Superdutypsd.com

 

Check all your suspension parts first with the wiggle test. I also would recommend a dual steering stabilizer kit.

 

I'm sure you meant to say to check for binding at full-lock both directions because that's where it will bind first and the damage will occur.
There needs to be some slack when the steering is centered because that is where the steering gears are most worn and removing all of that slack will bind the gears when turning.