Have you thought about this route
1) I-35 to Des Moines
2) I-80 west to I-680 in western Iowa (this takes you around Omaha)
3) I-80 through Nebraska, Wyoming, into Utah
4) US 40 /189 through Heber City down to Orem /Provo (avoids SLC)
5) I -15 through Utah, Nevada (use express lanes through Las Vegas)
6) In the outskirts of LA take I-210 around the "north" burbs of L.A.
Of course you need to keep you eye on the weather regadless of which route you take ... I-40 near Flagstaff was closed for about 12 hours on March 18 due to heavy snow and so many vehicles were in the ditch they closed the road.
2004 Winnebago Journey 39W - 2012 Buick Enclave
Present @home Home: Oshkosh, WI
We call our rig "Ernie the Journey"