Left car 2 days at dealership. Was able to make them hear the (very noticeable) problem.
They didn't find the root cause though and gave it back today.
The worst part is they asked to bring in my winter wheels, so I wasted half a day doing that so they could test if the problem went away after a swap. I have stock 18" wheels.
So back to square 1 - the BMW wheel change fee (I normally don't pay 100$ to unscrew and screw 20 bolts ...).
Will keep looking...