I've found from experience the southern route west you've planed is the best for avoiding most of the steep grades, But for the most part, east to west travel to CA is an up hill run until you enter mid way of Texas. The prevailing winds will also work against you most of the time as westerly winds will average a head wind of approximately of 10 knots. You may want to plan fuel stops accordingly.
I see you're thinking to go into CA from (I40). The destinations you'll planning makes it hard to bypass all the steep grade areas, as (I-40) will have a few to deal with, but I don't see an issue with narrow passes. I'm talking truck routes, main roads and interstates. If you're planning scenic routes, your map recon and other research is important.
A trucker's atlas should be used as part of your planning. Then you'll have the big picture and can set up your GPS to keep you on track. I'll cut my inputs short here so other experienced travelers can add more valuable information, as I don't have an answer to your concern with the shifting question. I've never had a personal issue with mountain driving, and find it mostly an enjoyable experience. Some may disagree, and that's where differing opinions clash.
Hope you have a great trip.
Dan & Loretta, US Army Retired Aero Scout Pilot
2012 Fleetwood Providence 42P Class A/DP
Spartan Chassis, 8.9L Cummins 450HP