With that EDD I would get the financing now. They usually hold the rate for 30-90 days. I thought I had time with my M3 for financing, got matched a VIN, started financing, and my delivery date window was over the weekend. I ended up having to reject the VIN because I would not get financing in time.
Also this thread has rates better than Tesla:
Funded today. Picking up car this afternoon. It took 7 business days once contacted by loan officer to get a check or wire transfer for Everence. How did you fund? Wire or check?
teslamotorsclub.com