I have the same issue in my 1997 E320. I agree that vacuum is probably the cluprit, just do not know where to start. Has anyone had this problem and solved it?

Vacuum loss is the problem & a VERY common one!

On the CLK try depressing the EC button & see if the center vents still close durning accel, IF not then the fresh air vacuum element is the problem!

The starting point is to find the vacuum block under the passenger under-dash panel & by using a vacuum pump check each vacuum line & vacuum element for leaks.

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I reference the WIS program and located the swithover valve block, the W210 with automatic air has 14 connections. Can you expound a little on the testing procedure using a vacuum pump. Any recommendations on a pump? I assume a rather inexpensive hand pump would suffice.

Does the dash need to be removed to access the vacuum elements?

According to WIS, it is located under the glove box. You probably just need to remove that cover above the footwell and maybe the knee bolster.