My wife and I will be taking a similar trip to yours, leaving Rockford, IL next Thursday, 12/17, and heading south and then west to Pomona, CA. In our case, we have to return again because of that "work thing."
For what it's worth, here's are major stops...these RV parks are all open year-round and had spaces available at least when we made our reservations.
17-Dec; Hollywood Casino, St. Louis, MO (Overnight in the parking lot.)
18-Dec; Big Red Barn, Carthage, MO
19-Dec; KOA Elk City/Clinton, Foss, OK
20 Dec; American RV Park, Albuquerque, NM
21 & 22-Dec; Mesa Spirit RV Resort, Mesa, AZ
23, 24 & 25-Dec; KOA Pomona Fairgrounds, Pomona, CA
26, 27 & 28-Dec; Off Grid near Onyx, CA
29-Dec; Sky Valley Resort, Dessert Hot Springs, CA
30-Dec; Mesa Spirit RV Resort, Mesa, AZ
31-Dec; American RV Park, Albuquerque, NM
1-Jan; Amarillo Ranch RV Park, Amarillo, TX
2-Jan; Big Red Barn RV Park, Carthage, MO
3-Jan; Double J Campground, Chatham, IL
We plan on heading south on 25 out of Albuquerque to bypass Flagstaff if the weather looks questionable, and while we've successfully taken the northern route through Omaha, Denver, and Las Vegas in an SUV in years past, we wouldn't personally attempt that in our MH this time of year. Sure you can wait out storms, but in our experience that wait can stretch into a week in the worst of conditions.
Good luck with your trip, and if you eventually post your itinerary, we'll watch for you en route.