I thought about that route, too, but I went with my method for two reasons:Agree with you approach except for:
Once you have the lowest number from those responses, send that number to ALL THE OTHER dealers and see if he's willing to beat it.
1) It's less work. In Nina's scenario she'd only have to contact one dealer after she got her low number instead of 9.
2) I think most dealers are going to tap out after 2 or 3 rounds, so waiting until you have the lowest new number possible before hitting up an individual dealer again would seem to be advantageous.