We found that T-Mobile has good coverage along major highways and most towns. Verizon is probably similar. You might have dead zones depending how far you get off the beaten path.
Both states are firearm friendly.
A shocking amount of the boondocks aren't boondocks, just somebodies backyard --- fenced off for ranching or somebody's 5 acre weekend getaway home.
Even small remote towns have gas stations and mechanics. Our Jeep blew a fuel pump is Salida, CO (population 5,200). The local mechanic had it fixed overnight (parts were shipped same day from Denver). If you are unfortunate enough to break down in a hick town, the parts you need will probably be available out of Phoenix, Tucson, Albuquerque, or El Paso. Just figure on spending the night.
Good luck. Have fun, and, post a trip report with pictures.