E39 540i/6 touring - Need advise on refreshing/diagnosing my suspension setup

[Japseguten]

Recently purchased a somewhat rough E39 540 with 230.000km "WBADR51080BX96307". Car feels unstable at speeds of 80km/h floating left and right on its own almost like being caught by strong wind. The steering wheel doesn't follow the floating direction, yet the linkage from the wheels to the steering wheel seemed tight when the car was in the air.

Some people say they remedied similar symptoms by simply replacing the shocks. FYI the previous owner installed 30mm Eibach Pro Kit springs on the original SE shocks and electronically lowered the rear self leveling airbags 25mm. While the TUV papers from Eibach say this combo is fine, i'm unsure since the car rides way softer than the lowering would suggest. He also replaced every bushing up front with cheap "OEM" replacements last year, so i'm considering putting some money in decent OE/Lemforder replacements here. Wheel alignment is also kinda off even after my local shop had a go, i'll try and upload a scan of the results later today. What do you guys think I should have a look at/diagnose/replace? I must admit i'm a noob at suspension, but I want to learn.

My 525i touring with original sport suspension feels lovely on the road in comparison so maybe a sport suspension retrofit would be a decent option?
Your input would be greatly appreciated!

[shogun]

Moved to E39 forum

[CPHES]

Somewhat rough... at the least, the springs and shocks are not a good combo. There have been threads that eibach pros are soft. If you combine that with a soft shock, it could be bad. The vin decoder says this is not a sport, so the original shocks could be valved for a soft ride.