Ford Discount Parts was nice enough to overnight me the replacement mirrors. I've installed the replacement mirrors and Door Modules. Unfortunately I don't have the heated mirror or puddle light functionality yet. I'm pretty sure the BCM needs to be told these things exist on the car.
I have some other things that I need to have worked on; and I'll ask the dealership to check the BCM when I have those things done. It will likely be two weeks before I get the car in; sigh.