being extremely rural outside the Phoenix/Tuscon areas,
Does Arizona really have that many rural whites? It's not northern New England.
No. Somewhere in the vicinity of 6-8% of Arizonans could be defined as white people who live in rural areas that are also heavily-white. If you want to include all white rural Arizonans regardless, the figure is probably a bit over 10% of the state.
And another consideration for any demographic analysis of the state: rural AZ isn't really all that much whiter on balance than metro AZ. We're talking about the difference between low-to-mid 60s for the former versus mid-to-high 50s for the latter. Perhaps the biggest difference between the two areas is that rural AZ is substantially more Native (and less Latino) than metro AZ.
