BMW Transmission/Warranty Issues?

Hello all! So I've just got back from a BMW Dealership in Mannheim, Germany. I've been having some problems with my 528i's transmission lately. Whenever starting off from a stop (i.e. red light, stop sign, etc..) my car would move backward a little bit and just "slam" into gear. This has been going on for a little over 6 months now. Anyways, when it first happened I took it to a BMW Dealership and they said there was nothing wrong with the car "alles gut" and that the problem was probably a one-off thing. But I've continually had issues, and I finally went to another dealership entirely. They are saying the car has been giving a transmission error code for awhile now (of course, iDrive didn't say a single thing but oh lets not forget that your DRL's are running dim). Also, the transmission oil is completely black and has a burning smell. Apparently the "clutch mechanism" isn't engaging properly and my transmission is "kaput". And i NEED a new one. They are saying 4000euros for the tranny and about 1500 euros for the labor. Here's my issue: BMW Germany is saying I should contact BMW North American since it is an American spec car, but I called BMW NA and they said its not in America so deal with BMW DE. These guys are saying I might be able to get a "Goodwill" coverage IF I had documentation from all the places I've had the car serviced at. Problem is, the dealerships in the states didn't mark the "Service Booklet" so they guy isn't budging. What should be my next step? I know everyone has said they've had to fight for warranty coverage, but I'm not even sure who to fight! I'm leaving for TDY next week, so I'd like to get this thing in the garage while I'm gone. Better to just take it to a Transmission Specialist? Thanks for any input.

Have BMW run a vin report. It will show all the work done on your car by a bmw dealership. I have never had one of my books marked by a dealer. Just does not really happen in America with computers