I've got no experience with the southern route, but we drive from Memphis to Vegas at least once per year and doing it in my Gen 2 is a lot more enjoyable than in my old 7.3L. Might suggest a hybrid route though for some nice detours.
If you went across to Flagstaff then went south you would end up with a really nice day or two trip. Just outside of Flagstaff is Cinder Hills OHV which has an easy / open place to open your truck up and play around without a huge detour. The lava rock area is where they trained the astronauts on the lunar rover and you can still see some of the old 'craters' out on the field. There is also the National Observatory in the middle of town which is a cool place to visit especially at night. Moving south towards Sedona is a beautiful drive and coming out of town you can go across the Schnebly Hill Road to I17 which is doable in a rental car and would be way more enjoyable in a Raptor. There are tons of 'Jeep' trails in the Sedona area that would be great in a Raptor, minimal skill required, and not too far from help if needed.