Around Arizona and New Mexico
The highways you are proposing are relatively easy. I've pulled all of them in an old Chinook motor home with a Jeep behind and then with my 25' Flying Cloud behind a 99 Tahoe and then a 2012 Expedition. Even up over Cloudcroft from Almagordo.
If you can, find a copy of Bransford In Arcadia by Eugene Manlove Rhodes and read it before you visit the area. Gene Rhodes was a real cowboy in New Mexico from his birth until the 1930s and wrote the best "westerns" ever. Guys like Zane Grey were phonies (he was a dentist from upstate NY).
The folks at the Border Patrol checkpoints are pretty much relaxed unless you look like you have 37 illegals in your AS. I'm a native of AZ and spend a lot of time in NM and have since the early 1950s.
Chuhhuniban - Grey Coyote (Tohono O'odham)
A late convert to Airstreaming after 30 years of white boxes and motorhomes, now we have the Tin Twinkie.