For Phantom Ranch reservations, I always try a week or two ahead when you usually get cancellations open up. Always call in the middle of the week in the afternoon. Once I get the dormitory bed, then I do my south rim lodge/ camp ground, rental car, and then air lines booking in that order. In one very hot August, while doing R-T-R, we just queried at the Phantom ranch for accommodations and they have an ac cabin available for the four of us along with dinner and breakfast. You just need to be flexible!