Your conversation sounds exactly the same as mine with my dealer over email. I wasn't in a big rush so time wasn't an issue for me. Just be patient and you'll get what you want. I had it all planned out on a spreadsheet as well and in the end their number was 10 dollars more than my number which I guess I didn't care too much about the 10 bucks a month. I started the conversation around the first week of December and the car finally got ordered & finalized right before Christmas last year. They aren't used to people being knowledgeable about leases I don't imagine so they don't have all the answers right in front of them. The majority of people just care about how much they need to put down and how much is their monthly payment, then they negotiate the monthly payment and not the total price of the car.
If you want the car.. just be patient. You'll get it.