I pulled the speakers out, peeled the spider back carefully, replaced both leads on both speakers, reglued the spider, and reinstalled. Everything is working again.
If I knew the hassle that the dealer would have put me through I would have just done this to begin with.
BTW, this is not a very easy procedure. If you have the same problem that I did and you aren't comfortable with a soldering iron and a multimeter then I'd recommend dropping your woofers at a speaker repair shop. It certainly would be cheaper than going through BMW.