So when I hiked it last fall Southbound, we had no issues they pretty much told us that worse case scenario we would have to spend one extra night at the rim on a waiting list. Also the AZT made a deal with the Park Superintendent that if you tell them you are a thru hiker that they will try and accommodate you in the livestock campground which is rarely utilized. I would not sweat it.
"Only those who will risk going too far can possibly find out how far they can go."
-- T.S. Eliot