It's been a long time since I drove a carbureted Benz, but I've messed with lots of carbureted cars of all kinds.
Although your vacuam advance may not be working properly, although you didn't say anything to make me believe that it isn't, I believe that your problem is one of two things:
It could be retarded timing, although it sounds as if you have set the timing, or;
The most likely problem is the accelerator pump in the carburetor. When accelerating lightly, the accelerator pump has virtually no effect. The accelerator pump squirts raw fuel in the airstream whenever the throttle is quickly opened. Whenever the throttle is quickly opened, there is a sudden inrush of air. If there is not a large addition of fuel at the same time, the engine will "starve for gas" and stumble.
Also, if everything else is correct, you could disconnect the vacuam advance and during acceleration, you would never know that it is disconnected. This is because the vacuam advance does not add timing unless you are not accelerating. When you are accelerating, there is low, or no vacuam. The vacuam advance is actually an economy device. Whenever you are cruising with a slightly opened throttle, the vacuam increases, which advances the timing. The advanced timing while cruising, provides lower fuel usage.
The easiest way to check the accelerator pump, is to remove the air cleaner, peer down the carburetor with the choke open, and of course, the motor not running. Snap the throttle open quickly, and you should see a stream of raw gas out of the accelerator pump nozzle. A flashlight is handy for this test. Remember that your dealing with gasoline, so it wouldn't be a good time to have a lit cigarette in your mouth.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
Over 800,000 miles in