Why did you need to prod them? When I ordered during the weekend, I got my order details with an order number Monday after. The "Type of Sale Code" in the order is "Private Individual" and "Status" is "Order Confirmed." Is that the same as yours? I got mine my Penske/Cerritos Jaguar.
To be honest, they were not very adept at computers. I had to help them, then they said they would email my official Order that afternoon. When it didn't arrive the next day, I reminded them.
It is a 4 pg JLR doc titled Order Details, gives an Order Number, options selected, my name, private individual, order confirmed, scheduling dates (my 'last changes' was 6/15, build 7/13, delivery 9/21, handover 9/26), pricing and 4 pages of options codes. It has a disclaimer at the end of each page that says it is not actually a purchase order and prices are subject to change.
So it is not binding. My deposit was on a second document, which says fully refundable.
I'm keeping the dealer private right now. If I understand it right, they were only allocated two First Editions, and both are now taken. I see black helicopters...