Oh, I have a tour for you!!!
i have done this a couple times as a one week supported tour. We do it in mid-April. It is very very hilly. The section from Alpine to Morenci has 7-8000' climbing and 13,000' descending and no services. It is also one of my favorite pieces of road that I have ever ridden.
I can't tell you about camping b/c we hotel it. Services are far-between, but there is probably just enough if you pay attention.
There are a couple of optional out-and-backs on this, note especially Mt Graham, that you could do w/o your bags.
http://goo.gl/maps/0K8H9