You are going through my neck of the woods.
I would recommend leaving Iowa on I 35 then pick up 36 west in Cameron , MO through St. Joe into Kansas at Concordia 81 south to I 70 west exit at Ellsworth, KS on 156 south/west to Great Bend 56 west to Dodge City then to Kinsley , KS 183 South to Greensburg, KS and go west on 54 follow 54 to Santa Rosa, NM then 54 goes south towards Alamogordo. At Alamo. pick up 70 south/west to I 25 south to I 10 west to PHX.
There are no big Mt. grades going this way and all the routes are good roads with not much traffic and RV friendly !!
I have run all these roads many, many times for many, many years.
Today in South east NM the sun is shining and the sky is bright blue......Have a great trip whatever way you go.