Ignore EDD until you get a VIN. It means nothing. You will get your car in june.
Might be talking about me: I've had a VIN since 5/16 and mine has slipped 1 day at a time for 6 days straight starting at my original EDD up until now: my original EDD was 5/27 - 6/3 and it has crept up to 6/2 - 6/9 today. So apparently even when you DO have a VIN, it means nothing!