Randomly checked the app again today, and to my surprise there is another EDD update! Once again a short two-week window, and once again no VIN. Having gone through this song & dance once before, I reached out to my SA, who said they don't see anything in the inventory matching my configuration.
But on a whim, I went and checked the New inventory within 200 miles of my location, and it almost appears as though the Model 3 section is broken for all new cars, and for specifically just black paint in the Used section. So I'm unsure how reliable that Inventory list is.
In any case, I'll ignore this new date unless I get messaged with a VIN next week.
PS: I've seen some people manage to "pull" their VIN early, from looking at some source code somewhere. Can someone explain how and where exactly is that done?