I usually take two or three days to drive from just north of Tulsa to Lansing. There are hundreds of possible routes with different places to stop along the way.
What have we done between here and Lansing? A day in Hannibal on three different trips. Visited Popeye's home town in Alton, Amelia Earhart's Birthplace museum in Atchison, Gateway Arch in St Louis. There is Will Rogers birthplace museum in Claremore, Indianapolis Motor Speedway Museum and the transporation museums in Auburn. Twice visited the RV Hall of Fame in Elkhart and toured RV factories in Middlebury and Nappanee, visited flea market in Shipshewana. Might visit Walt Disney's home town in Missouri (or maybe Patton's or Montgomery Ward's, all three on the US-36 corridor to Hannibal). Been to the Living History Farm in DesMoines, windmill museums in Pella. The trip to Lansing lets me visit either Madison or Springfield in three states (different routes).
I can make this part of the Lansing trip in one very long (17-18 hour) day on the fastest route (which is I-94 to I-80 to I-55 to I-44) or I can choose among other routes up to 20 hours, spread over two or three days, and see something different each trip, one tourist stop each day. When I do this as a two-day trip, my stop is somewhere between Hannibal and Decatur going east, Hannibal and St Joseph going west. Stops for a three day trip depend on what I'm visiting, where I spent the extra day touring.
Beyond Tulsa (which some people come to visit for as much as a week for what is there) you will have things to drive past like the western heritage and aviation heritage museums in OKC, Palo Duro Canyon in the Texas Panhandle, two big Route 66 museums between OKC and the Texas state line, and all of New Mexico.
With the amount time you are allowing, you will have to take the fastest route, which limits the places you might visit. You will have no time to visit anything on the way, so you might as well fly over it. For me, even if I was driving, if my time was so limited I would take my car or truck, so I could move faster safely and not lose time getting in and out of campgrounds or RV parks each day.
Make it a two week trip, and it is worth doing by RV; make it a modest loop, one route going down, another going back.
In August, expect daily highs 90-105 F through Illinois, Iowa, Missouri, Kansas, Oklahoma and Texas, without seeing anything cooler until getting some altitude in the Rockies in New Mexico. Summer heat on the Great Plains tends to break some time after Labor Day. I find it difficult to keep the inside of my class C much lower than 85 F running in the full sunlight at this time of year, running both front and back air conditioners. You'll need to be sure your generator is in good condition, up to running 10-16 hours a day.
For that matter, it is also difficult to keep the inside of my van, or my daughter's minivan, comfortably cool when it is 100F in full sunlight, although in either one the rear A/C will easily freeze you out in Michigan summer weather.