I had a E320 and my dads C230 that I would press on the accelerator and the engine would rev all the way up with very rough shifting, and it felt like it was going to stall.

The Check engine light would come on too.
Turned out it was Mass Airflow Sensor. Easy 5 mins replacement.

Buy the part yourself online and replace yourself.

But hard to believe check engine light comes on and there is no diagnosis code with the OBDII scanner...

It looks like your dealer is trying the trial by error method...
I would get a 2nd opinion at another shop...