My 300sl 1987 suffers from wobble or shake felt throughout the entire car, not just through the steering. This is especially noticeable with the hard top off (not really surprising). Lots already done to try and resolve ie.
- new subframe mountings
- new tie rods
- new dampers (Bilstein) all round
- new lower front wishbone joints
- new steering damper
- new idler arm bushes
- new wishbone bushes
- all wheels aligned and balanced by MB
- play in steering taken up by steering box adjustment nut

Whilst the handling is crisper than originally the wobble or shake problem hasn't gone away. The problem is most noticeable when driving on rough potholed roads the potholes seeming to initiaite the vibration by giving the suspension a 'kick'. On undulating roads car tends to wander somewhat.
Nothing, other than dampers, on rear suspension considered so far.

Is there anything here that I should look at?
I've heard of cowl or scuttle shake. Can this be fixed if this sounds like the problem?

Any suggestions most welcome.

Thanks.

Almost all convertibles have a "bit" of Cowl shake, sounds like yours is worse than most.
Firm shocks will amplify the problem, so will low profile tires & high tire pressures.