Driveline vibrations are a weird thing in how they manifest and reverberate through the vehicle.
I believe most BMWs use giubos to connect the driveshaft to the transmission? That might be enough that it will isolate the vibrations from the shifter. I can say that I had a u joint cap in my pickup's rear driveshaft seize up a few years ago and cause a vibration. I could hear the terrible vibrations through the cabin and they were awful but couldn't feel anything through the shifter. And this has the driveshaft directly bolted to a yoke on the transfer case.
If the frequency is like 15-20 times a second (depending on tire circumference), it's rotational to the wheel/hub/rotor/cv ... etc. If it's really fast like 60times a second ... it's probably driveline related. The driveline spins significantly faster than the tires.
I've been fighting a driveline vibration issue in my Grand Marquis after swapping to 3.55 gears. I am running an unsupported config from ford - long steel driveshaft with 3.55 gears, ford never supported this for anything but 2.73 gears. The gearing I have now would have come from the factory with aluminium driveshaft / short tailshaft or the longer tailshaft / shorter steel driveshaft. If I am on the throttle or fully off the throttle between 65 and 75 I have no vibrations. But if I let up and there's a moment where there is no load on the driveshaft, it vibrates. The vibrations come from the front of the car, not underneath or from the rear.