My recommendation would be to go through a broker at this point. Given you need a car ASAP and you don’t seem super familiar with leasing, going through a broker will save you effort, time, and money
There are lots of resources on this website for those willing to put in the time. There are many discussions on how to negotiate, by email or otherwise. If you propose a range they will always take the lower end of the range, and then you need to be willing to go ahead or you’ve lost that dealer forever (and wasted everyone’s time). It sounds like you had already agreed to a number with a previous dealer, and you ended up not going ahead with that one. That burns the dealer for the rest of us too.