Thank you all for the suggestions!
John: It looks like Red Rock Canyon State Park is now privately owned, and renamed to Red Rock Canyon Adventure Park (https://www.redrockcanyonadventurepark.com/). Depending on how far we decide to travel in a day, that looks like an interesting option.
WhatDa: We didn't have much choice in the pick up date (July 3) but a call to Oliver TT this morning left us feeling a relieved. A skeleton crew will be working on July 5 if we need a repair. Plus, worst case scenario, we will be able to park at the sales office if we need to wait until Monday the 8th. Luckily, my husband is handy, logical and resourceful ;-)
Mossemi: Your HH suggestion was timely and prompted me to get a membership. There are some intriguing locations scattered along the way that look like wonderful possibilities, especially for a short overnight stay without having to unhitch. Much appreciated.
Overland: KOA is a good option, thank you. I usually don't look for KOAs using my online searches, but it's good to know they're plentiful along I-40.
We'll be fine as soon as we get solidly "west" (New Mexico, Colorado, Wyoming etc.) as we are used to boondocking and exploring in that area. We're just not used to having to plan so far ahead and make reservations. We usually just move with the weather and have learned to show up early if we need to score a spot at a developed campground.
Many thanks~ Chris and David