If you do not mind back roads take I-10 to US 70 in Las Cruces, NM. Then take US 70 to US 71 in Ark. US 70 in NM goes over one pass around Ruidoso, NM but it is not steep up or down and, unless a storm passes through, is a good 4 lane most of the way.
There are other routes to avoid cities like US 62 out of El Paso to US 380 in Brownfield, TX which would have no passes worse than Texas Canyon near Benson, AZ on I-10
5er/2500Duramax/18ftBoat