I know you are excited to pick up the car, but you are the customer. Let them sweat it. They are in a push to get sales in Q3? Fine, then it is on them to get the info you need to get your loan and insurance strait. I was bracing myself for this same exact situation based on other comments on the board.
I live close by the SC, so I would have casually walked in on my delivery date without check or insurance - "You want to get paid today? Huh, nobody sent a VIN. My credit union is closed on the weekend. How about you guys get your *sugar* together? Call me sometime when you find the VIN. Enjoy your day!"
Fortunately for my situation, the IDA got me my VIN 4 days after placing the order since mine was already built. TBD how pickup goes next week, but at least my docs are already in order. What a PIA for you - sorry you have to deal with that.