We have done 2 trips to the Grand Canyon using the route you mentioned. Between the two trips, we used the following campgrounds, some of which may fit your timing:
Casino Queen RV Park, just east of St. Louis.
Tulsa NE/Will Rogers Downs KOA, FHU sites in a parking lot for the casino/race track. We had breakfast in the RV watching the horses having their morning exercise on the track.
Amarillo KOAGrants/Cibola Sands KOA - they have a short trail through a lava field adjacent to the campground.
Holbrook/Petrified Forest KOA - for a tour of the Painted Desert & Petrified Forest.
Meteor Crater RV Park - for a tour of Meteor Crater.
Lastly, consider driving north on route 89 and enter the Park on route 64. Route 89 passes
Sunset Crater and
Wupatki National Monuments, which are worth a side trip. Route 64 has views of the canyon of the Little Colorado River and takes you along the Grand Canyon Rim on your way to Trailer Village.
2003 Winnebago Minnie 24F - Ford E-450🙂