I've mentioned before that I have steering play on my W126 as well. I finally took it to my new favorite mechanic since it was wearing the insides of the front tires.
Well, the mechanic found a number of things that 3 others missed. First, my motor mounts were heavily worn and one was broken. A shock had failed as well as a bushing. He found out that my wheels are not correct for the car. They look right, but the offset is wrong. Finally, W126 cars can a the wheel front/back separation adjustment. Mine was too short by 10mm.
So, all previous chassis crimes were corrected as well as a new steering pump since the old one leaked badly. The car was taken out for a test drive and not a mile from the shop, the hood popped open which destroyed it and the hinges. Evidently, the hood is aluminum and thus crushes easily. Luckily, the mechanic had another hood and is putting that on now. I have little doubt that the car will handle like new now.