Ok... a couple comment on your locations... The two campgrounds on Oak Creek Canyon will be crowded. Really crowded. And there is no unimproved/free camping in the canyon at all. There are some primitive camping areas along 89 before you drop into the canyon, but nothing after that.
The campground at Ashurst lake is on top of a plateau and is mostly scrub juniper. Not a lot of shade if your looking for tall pines and whatnot. It will also likely be completely full due to the expo.
The last one on the rim I'm not terribly familiar with. Lots of better options further up the 87 towards Mormon Lake though. From Clint's Well on up there are miles and miles of forest service roads and some FS campgrounds as well.
I'm sure you'll find something up that way though!
_coder