Can you give us some road numbers you plan on checking out? Perhaps someone here has driven them. Or a particular area of the White Mountains you want to stay?
A very good road atlas we've used for the western states, including Arizona, is put out by Benchmark. It's vastly superior to the Delorme atlas. Go to an Arizona book store and you can find them for sale in the mapping area. Many public parks also have them for sale. Each atlas contains only one state so the print is large with lots of detail, especially for backroads and public parks/sites. I think you'd like it. That's how we decided on many of our boondocking excursions with our 40' motorhome. You do have to do some research first. Word of mouth from other RVers is a good resource and as always, Google is your friend.
We traveled down many, many good gravel roads and never had a problem. Only a couple times did we disconnect the Jeep to explore the road first but even then the road turned out to be a good one. With your small trailer I doubt you'd have an issue but don't try it during monsoons. :)
There are gorgeous areas in the White Mountains. You'll find that perfect spot!