It's time to at least be a little bit more of a "squeaky wheel" with these guys. Put some pressure on. If they tell you the engineer is coming in, ask when. If they tell you it looks like the transmission, ask how soon will they know, and when can it be repaired/replaced. It doesn't take a month and a half for someone to come in from Germany. I know. I've made that flight before--easily doable in a day. Call them every day, if you have to, to light a fire under their arses. Be a nuisance.
Definitely, definitely, as a previous poster said, take pics. They should not be neglecting your car like that. At this point, I would definitely have a conversation with the service manager, if you haven't already. Let them know this is no way to treat a customer, and especially no way to treat an M car. I'm really sorry to hear of your misfortune, and I hope you are taken care of very soon.