Have a look at page 46.7-220/8, in the service manual, chassis and body series 123 volume 1 and you will see a cut away for the steering box.

It shows that the gear on the pitman shaft is tapered down at the top and that the working piston, the other gear that meshes with the pitman shaft is also tapered. What the adjustment screw on the top of the steering box does, is move the position of the pitman shaft on the vertical. By moving the pitman shaft up the slop/lash can be removed from the gear thus eliminating almost most of the excess play in the steering box. These boxes are old and well worn so total elimination of the play is high hope.

The previous owner of my 240 bought a rebuilt steering box for around 400 bucks. The box was rebuilt, but I don't think the worn gears (pitman shaft/working piston) was replaced. The play was massive when I got the car, realized the installer of the box did not adjust it and so screwed the top adjusting bolt out a bunch. Play was at a minimal but has started to get worse over time. I checked the PS filter/fluid and it seems the installer changed nether and it was full of grit and crap. Its flushed now but I think the damage was done.

Now if we could just find the 3rd version of the box (found on w201) that fits out cars, they have automatic play compensation.