Spent several weeks setting up a post retirement route, basically going across the top of the country to WY, then down to AZ... Best laid plans :( I now have a medical procedure schedule planned...
You didn't say where in AZ you were heading... Snow along I-40 isn't unheard of in October.
The routes mentioned to Flagstaff work for Phoenix. Definitely head to I-70 at IND instead of anything close to Chicago. Bring cash for the OK Turnpike...
If your destination is Tucson or Yuma, then you'd be better off heading down US-60/US-70 from Amarillo to Las Cruces, especially if the Balloon Festival is going on. It's a fairly interesting drive the more you get into South Central NM.