Labor day would be dicey, unless you make camp a day early. Like most of Arizona, (in my opinion anyway) recreational and wilderness areas are very under utilized. A high clearance vehicle or SUV is the key to avoiding the unwashed huddles masses. But even in the popular places, like 4 Peaks, or the Mogollon Rim; a trip doesn't go by, without Susan or I muttering to ourselfs: "Where are all the people?" By the way, this location doesn't require a high clearance or SUV vehicle, it has in years past, but the roads in decent shape this year.
OK, my advice for Labor Day or Memorial Day . . . . . stay home and save your camping trips for virtually any other weekend.
Lastly; When driving on 260, in that area be on the lookout for elk, they are everywhere, and hitting one is a serious accident. I read that on 260, in Sitgreaves last year, there were six Elk accidents, per mile of road.
Mother nature seems to like humans, and not just because they taste like chicken