Panzer, It's been more than 5 years since I took my steering box apart and resealed and adjusted it, so memory is kinda stale. However, I can relate a few things.
My '91 300SE runs straight and true, until there is any wind, then it wanders like a drunken sailor. This started about 10 years ago as I remember, and I tried for over 5 years to find the problem and fix it. EVERY part of the front and rear suspension has been replaced, with no help. I ran out of things to try about five years ago. Biggest help was the steering damper.
I have begun to wonder if it is related to the 16 inch wheels I installed about 10 years ago. They have the correct offset, tire diameter, etc; but who knows?

3 turns on the tension adjuster seems like a heck of a lot. When I first adjusted mine at about 80K, I definitely noticed it tightening up before 1/2 turn out. The friction surface is an organic washer, maybe it is shot in yours.
As you know, with the engine off, about 2 inches of play at center is normal; it goes away when the pump is running. Checking friction can be done pretty well by just jacking the wheels up; you can feel the difference the adjuster screw is making. Better, of course, is to pulll the pitman arm.
As you probably know, the friction is supposed to be higher near center (approx 120 NCM), then decrease as the wheel is turned L or R.

Don't know why the centering is off; may be tied to the 3-turn issue.
There is a bolt under the box near the pitman shaft that can be removed, and a pin can be pushed up into the box to locate and hold the center position (there is an indention in the gear that the pin will slip into when the gear is dead center). You might try that; it's possible your steering wheel is not set at dead center on the steering shaft?

When my box started to leak, I took the opportunity to buy a repair kit and take it apart. it was really pretty easy; of course I didn't take the whole thing apart. But while it was on the bench, I did some math with a rod and a hammer head, and did the friction adjustment per the book. result; leak stopped, friction correct, still wanders in the wind.

Good luck. If you find the wandering problemit, let me know; I'll be your friend for life.

DG