Still waiting...
With our previous two Model S orders, the delivery specialist was not always a good source for information. Sometimes we'd get more information from our Tesla Account page or status updates sent to us from Tesla.
Tesla is likely very close to the 200K US delivery trigger - which is probably why they just shipped a large number of Model 3's to Canada, to get those cars delivered in this quarter, but not count against the US tax credit trigger.
While our DS thinks the car will be delivered in early to mid June, I would not be surprised to see that slip into early July, if that's what it takes for Tesla to push the 200K delivery into early July.
About the only thing we should be able to count on - cars that have VINs today will likely be delivered by mid-July.
We're still hoping for early June - since we plan to take some family trips in June, and the extra seating in the Model X would be useful (compared to our S 100D).