Thanks for the thorough update.
So some quick comments:
1. I suspect that both new and remanufactured engines ship from Germany. Just FYI. I am actually not as concerned as others may be about a 'reman' that comes out of a BMW plant, but if you are, make sure you know what you are getting. The dealer may be shorthanding it, but maybe not.
2. I would (and I do/did, every time I have a dealer visit for warranty work) insist on a copy of every single document in my service record- all the juicy stuff that is usually stapled to the work order packet and filed away or copied to BMWNA. They will have you sign some cover sheet, and you get a ridiculously short "official" record .... but you want the entire record (well, I do). I want the DME print outs, everything. I simply say, sweet as pie to the gal processing the paper. "Could I just get a copy of all this before I sign for it?". I've never been refused. Think of it like medical records- it is your car, you have a right to it. If issues come up later with tranny, etc, your having the work history might be invaluable...