Really glad to find others with my mini's ailment.
My best guess is the clutch plate as well. I think it is glazed over...wearing out. The reason why there are people having trouble replicating it at the dealer is because it only happens when the flywheel and clutch plate are cool. When you get to the dealer, all of that stuff is warm.
My "chewbacca type noise/ship's horn" only happens at my first few starts in 1st gear in the morning...on a cold engine.
I'm not really surprised to have this happen to mine because of the 60K miles on it, and the fact that it is a
JCW that is driven as it should be driven.
It sucks, but the only way to have the dealer hear the wookie is to leave it overnight and have them ease out the clutch pedal as the transmission engages 1st in the morning.
Good luck to all, and I will check back to see if my clutch predictions were correct...as I'm out of warranty.