Classic MB like ours has no clearcoat. It is Glasurit paint used by MB.
From what you are talling me of the basecoat and assuming you still have factory paint on your car. It should be able to be polished. I know what you are talking about... it is dull looking now and fine sandpaper feel to it.
With a washed car, I would first start out with clay bar treatment... You can buy clay bar kit at any place... all under $20 a kit. Use car wash soap diluted if you run out of 'lubricant. Go over the entire car with it. No pressure needed... some light pressure and go over and over. This process takes one hour or less. Dry the car.
I would then use Fine Cut #2 and use the real randome orbital car polishing machine... like Griot Garage's machine (I have one). Go over the entire car and wipe off.
Then I would use Polishing #3 and go over the car with the machine and wope off.
I would use clay bar gain and wash the car.
Lastly, I would use Paint sealant or good car wax of your choice.
Let me know how it looks afterward.