If you're doing this in a car... consider AZ-77 up to Globe, and then US-60 over to Socorro, NM. Time-wise, it's longer, but you're going to see scenery you'll miss by driving around the White Mountains...
US-60 goes via the Salt River Canyon between Globe and Show Low, and also thru the middle of the Very Large Array radio telescope. It's one of those out of the way place many people never see, let alone stop at for the free self-guided tour...
I don't mind that type of drive with the Class C, but it can make some people a bit nervous... In a car or truck, I wouldn't think twice about going that way.