In order to park at the field with the Airstream group (no hookups), you need to get on the list months ahead. I think the list opens in February and can fill up by May. It is full now. You can watch the Rally Calendar on this site for an early post on where the thread is for the current year.
You can get info from the organizer at BalloonFiestaRally@hotmail.com
As for getting a spot at Kirtland, they have a large overflow area with no hookups. I've stayed there several times on other business during the Balloon Fiesta dates and always been able to get a spot. The last time was 5 years ago, so I don't know if they have made changes since then.