Here are my thoughts.. I don't think it's the transmission or TC.
The M62tu motor torque and power comes on song circa 3500rpm anyway. The lower end power is controlled by Vanos. Mine had (and is happening again) several years ago the same symptoms as yours. I had no codes but a search of Internet pointed to Vanos solenoid. I replaced the one on the right side as you look from the front and it transformed the car.
Another symptom I had was while driving on cruise control then turning it off, the car decelerated like I had applied the brakes.
Something to consider.