UPDATE: So on the return trip, we just happened to be walking out when the shuttle was pulling up, so no wait. Just make sure you tell the driver you are going to Sundance (Sundance contracts "Sky Harbor Parking" shuttles, and only some of the drivers are designated to go to Sundance). Driver was helpful and polite. Tip them if they're good!
Back at the lot in 5ish minutes, only to discover I had left my interior lights on the past 5 days.... Again, the lady working inside was of no help, and told me that all she could do was "call a shuttle driver and see if they have a box".
Not sure what that means.
Luckily another family got dropped off as we were walking back to the car, and they were able to jump our car no problem.
Checkout was easy, I pulled up to the window and handed her my receipt I printed at home, and the the ticket the machine gave me when I pulled in last week. If you follow the directions (not really laid out that well) it's a simple process.