I think you can do it. The wife and I did 6,130 miles in 17 days on a motorcycle last year. It is all in how you plan the trip. We stopped every 100 miles for a short break. Probably not necessary when riding in a truck. One thing we did was a light snack to start at 7 AM (think pop-tart) drive until 9 AM, stop and eat a hearty breakfast. Back on the road by 10:30. Pee break and snack around noon. By 2 PM you will be ready to eat another full meal. As long as you don't try to go tank to tank on the truck everybody will be fine.
Don't forget about the badlands. They look to be about 2 days travel from you and would be a good one day stop to recharge and get a glimpse of the variety of terrain that lies ahead on your adventure.
