Here are a couple of other possibilities:
Phoenix to Grants, NM: Blue Spruce RV Park, about 6:30 hrs.
Grants to Amarillo, TX: Oasis RV Resort, about 6:20 hrs.
Amarillo to Checotah, OK: KOA, about 6:40 hrs.
Checotah to W. Memphis, AR: Tom Sawyer RV, about 6:35 hrs.
W. Memphis to Harrison,TN: Caney Creek RV, abouit 6:40 hrs.
Then about 5:20 hrs. on to Charlotte
Phoenix to Las Cruses, NM: KOA, about 6:45 hrs.
Las Cruces to Odessa, TX: Midessa Oil Patch RV, about 6:20 hrs.
Odessa to Arlington, TX: Treetops RV; about 6:00 hrs.
Arlington to Vicksburg: Ameristar Casino RV: about 7:00 hrs.
Vicksburg to Tallapoosa, GA: Big Oak RV, about 6:50 hrs.
Then about 5:30 hrs. on to Charlotte
Comments about first route. This puts you through Memphis where there is ongoing construction and also Nashville and Knoxville.
The second route skits on I-20 south of Dallas/Fort Worth. I have always found it full speed limit around. There are many choices of RV parks. We have stayed at Treetops, KOA, and Cedar Hill State Park. All were fine, just different. We have also stayed at the Ameristar Casino in Vicksburg and the Big Oak in Tallapoosa, GA. Birmingham is an easy city to navigate on I-459. I've never had trouble in Atlanta, but timing is important there.
These are just examples based on one assumption: that you are just making the trip and not visiting tourist attractions. If not, that could change everything.
I've been over all of the second route and most of the first--except through Oklahoma on I-40. I will be glad to answer any questions you may have about these routes or other possibilities.