A case of beer? All right, you’re on!
After reading through the thread again, I think there are at least two different noises being talked about, though.
My car developed a kind of rubber/metal squeaking/creaking noise when driving over big bumps right after installing the Bilsteins. With the Eibach spring / OEM damper combination I had on before, which lowered the car more than the Bilsteins do, there was no noise. Immediately after replacing that combination with Bilsteins and OEM springs the squeaking was there. I disassembled everything again, made sure every piece of rubber was where it should be, that the springs were perfectly centered in their seats, I preloaded the suspension, torqued every nut and bolt exactly to spec, greased all the bushings with silicone grease, centered the sway bar, ensured the battery tray could never contact the sway bar, etc. The squeaking was still there. After hearing that noise, my service manager said that was the typical cold Bilstein squeaking he knew from his Alfas.
The noise you posted about is a clicking though, not a squeaking. My car slowly developed a clicking from the right front wheel area years ago when I had the Eibach springs and OEM dampers. Just as you describe, it was play between the steering gear box and the rack inside it on the passenger side. Since the bushing in the steering gear box cannot be replaced, I had to replace the entire thing. With the new steering gear box, the play was gone and so was the clicking. Now, years later, I’m starting to get play at the exact same point again and the metallic clicking is starting to come back.
My hypothesis regarding the clicking: when the car is lowered, the tie rods and steering rack are no longer on the same plane. When you lower the car, the steering rack is lowered relative to the wheels, so the tie rods point down towards the steering rack. Bumps and even just steering will tend to exert greater vertical forces on the rack. That will wear out the bushings inside the steering gear box faster than if the car were not lowered. If the bushing on the passenger side already has some play maybe you don’t get the clicking very much if the car is not lowered because there are not many vertical forces on the rack. When you lower the car (for example with Bilsteins), vertical forces will be exerted on the rack and if there is play, you’ll notice it with that clicking noise.
In my case, a new steering gear box got rid of the clicking on the passenger side, as you described. I have yet to find a cure for the squeaking, though.
Now about that beer…