I’m following this with interest. I’ve observed similar behavior occasionally on my M3W, I coast to a stop in neutral and the engine is idling at about 2000 rpm, but as soon as the wheels stop turning it drops to normal. This behavior is intermittent, and I have wondered about it, but not tried to solve it yet.
Those are exactly my symptoms. I have an updatable ECU so will have a look at Protune later, I need to experiment though as I suspect it only happens when the engine is cold.