The route I take to Yuma AZ every fall is nice, avoids high mountain passes and heavy interstate traffic.
From Sioux Falls go S on 29 to St Jo Mo. get on 59 to Atchison Ks, mostly flat and runs beside the Atchison, Topeka and the Santa Fe Railroad. To Topeka Ks to Wichita Ks on I-335 to I-35.
Now the good part, Pick up 54 to Liberal Ks to Dalhart TX and then on into Tucumcari NM.
This is the Snow Bird Route for those who go S for the winter to NM and AZ.
If you want to climb Mountain Passes just for the heck of it, I for one find no redeeming benefit for doing do. Go the way you were thinking.
Tucumcari is on I-40. There are plenty of RV Parks along the way for over night stays cheap.
We normally take 6 days from Waterloo Ia to Yuma AZ 1800+ miles. Albuquerque NM is a short jump from Tucumcari. The whole route is mostly flat and relatively low traffic compared to an Interstate.