I had the same problem years ago on my 98SE.
Freeway speed, drive over some uneven section of road and violent shakes, scary, dangerous and embarrassing.
I would describe it as tank slapping, (a motorcycling term for a similar scary thing that happens to riders from time to time)
I changed the suspect steering damper first up, as it was on the way out, but like you, still had the problem, as bad or worse.
After reading the numerous posts here and considering all the different things others have tried, I can only come to one conclusion:
The inherent design of our truck's front end is such that, with a particular combination of wheels, tyres, toe in, shock absorbers, and steering box adjustments, there is a natural resonance , which at a certain critical speed the front end can be set off like a bell ringing. Set off by a disturbance, a bump.
Once it starts, it just self excites and keeps going, until you get away from that critical speed.
You can be fortunate, in that for your car, the critical speed for resonance is so high you never reach it.
Others are not so lucky.
Changing components can change the resonant point so much, that it no longer is an issue, or if the components you change have basically the same characteristics, the problem remains.
As with all resonance circuits, a good damper can kill the vibrations or prevent them from starting up.
Some cars will have the problem worse than others of course, and then even a good damper may not help.
All of the above is just my theory of course!
Did you change the steering damper with a genuine one or an aftermarket one?
Why I ask is because after a lot of checks, similar to what you had done, for some mysterious reason, I decided to pull out the new damper and check it on the bench.
It was an aftermarket one, from the UK, (I am in Australia).
The damping was good and firm in both directions but when I applied small back and forth movements rapidly, there was a small amount of movement possible which was not damped at all. About 10mm to 15mm.
That was enough for me. I bit the bullet and purchased a genuine article, at about twice the price.
That was one of the best decisions I have ever made,.
After installing it, no more violent shakes, ever!
I know that it does not fix the underlying cause, but bear witness to the many who have effectively had to change the whole front end to get a result.
My problem may have been different to yours of course, but, I have done over 100,000k now since fitting the new genuine steering damper, and no more death wobbles, even once.
Good luck and cheers.