Mercedes W126 vibrates at speeds over 120 km/h

all

I am at my wits’ (and budget’s) end

My recently acquired Mercedes W126 has a vibration which stats at ±120km/h. It is dependent only on the driving speed, whether in-gear or coasting, under power or braking, 4th, 5th or neutral. I have had the mags, which are genuine Mercedes, refurbished to remove all warping and ovality; the tyres are brand new and the wheels have been balanced several times now; I have had the propshaft rebuilt and replaced the centre bearing and the guibos; I just had the entire front suspension and steering rebuilt along with new shocks, wheel bearings, brake discs and pads. All to no avail.

The vibrations are at much lower frequencies than the engine (±2800rpm, 46.6Hz) and propshaft (3500rpm, 58.3Hz) speeds, more like the wheel speeds (±1000rpm, 16.7Hz). The vibrations feel like they are phased: sometimes the car shakes transversely, sometimes the car shakes vertically, sometimes around a gentle turn the vibrations even almost disappear completely.

I don’t believe in throwing money at a problem until it goes away. I want to know what to look for and how to look for it, so that a proper diagnosis can be made and the cause of the problem be resolved. I am open to advice and suggestions.