Mine got through production last week very quickly, was put on a truck, and also got to Chicago very quickly.
The original stated delivery window was the same as yours, then they narrowed it to 3/26 - 4/2. Delivery is now
slated for beginning of next week, so that's even toward the beginning of that narrowed window. In fact, had I been
able to take it, I think they would have delivered it tomorrow or even today. They seem to be getting this whole
production and delivery process down.
My DS wouldn't officially confirm this (the party line is "we won't rush any part of the process"), but it looks like they're
trying pretty hard to get as many cars delivered by the end of the quarter as they can. So I think you can be optimistic
about by-the-end-of-the-month delivery.