Mid to late May is a good time to push off from California, but you may not be aware of the climate regimes in the West.
Imagine a bookshelf with fat, hardback books - yeah, I know, books are so 20th century.
Along I-70 in May there's not much difference in temperature between St. Louis, Indy, and Columbus.
Sure, there can be storms in one place and not another - but the weather is similar.
In the West climate zones shift radically on a west-to-east axis.
It can be 60F in San Fran, 90F in Sacramento, 40F with a chance of snow in the Sierras, and back to 75F in Reno.
Further south, it can be pleasant in Ventura - and broiling in Needles - then chilly in Flagstaff.
Attached Prism Climate Map - Oregon State Univ.
Because you will be in the Mojave in late May - you should expect high temps in the 90s - even 100+
But when you get to Flagstaff - you can expect low temps near freezing.
Western Regional Climate Center data -
I am not sure what your specific stopping points are along the way.
Not sure why your endpoints are Morro Bay and Wrightsville Beach, but I'm sure you have your reasons.
I did see SRAM offices in Colorado Springs, Chicago, and Indy.
Can't tell if Flagstaff, Omaha, Charleston, WY, or Raleigh are fixed points.
(From the map, it seems that Raleigh is.)
What are the places you must hit in the West?
Because there are much better ways to do it.
And why miss the Grand Canyon or other spectacular regions of the West, eh?
Here's one example - East of Colorado Springs:
Take Hwy 94 due east to
US 40 east into Kansas to
Hwy 25 to Colby
Low traffic once you get 20 miles east of the Springs.
Enough small towns for the essentials.
Way more scenic than a service road next to I-70.
Best - J