I drove from Flagstaff through El Paso and on to Louisiana by way of the Hill Country at the end of October.
My route was somewhat different, but one you may wish to consider in reverse. My route was I-40 from Flagstaff with stops at Meteor Crater, to Holbrook, then Hwy 180 to the Petrified Forest NP south entrance where I spent the night at the free campground, and on to Saint Johns, AZ (a surprisingly scenic little town), south on US 191 to Springerville where I spent another night, then on south to Alpine, where I turned onto US 180, spending 3 or 4 nights in the Gila National Forest area, and on south through Silver City to Deming.
The vast majority of this route was good road, with the exception of a few miles of rough pavement just outside Holbrook, not bad road, just roughly finished pavement. There was also a few miles of sub par highway in the Gila national forest, from the NM state line down to around the intersection with NM 12. The section throughout the the Gila National Forest is scenic, a bit winding with a speed limit of about 50 mph. Just be aware there are limited pull off spots for big rigs between Alpine and Silver city, and no good fuel stops, so make sure you have a full tank of fuel before entering this stretch.
2002 Safari Trek 2830 on P32 Chassis with 8.1L