Interesting posts. We did just under 6,000 miles out there from central Illinois this summer, not in the months you are asking about. Visited all the places you are planning. You won't be sorry, it is a wonderful trip to say the least and we will make that run again.
The only thing I will add, we were able to park along the side of the road in several spots and get out for some photos of me making/throwing snowballs. My only advise would be to stay away from a far northern route for the months you mentioned.
If time is not really a factor, New Mexico, Arizona, parts of Texas have much to offer en route to some of those California destinations. You could still do Montana, Wyoming, Nebraska coming back. Or reverse that and come back through the southern route.