We traveled that route twice last year on the way to St Louis. We fueled at Winslow AZ., Amarillo TX., and OK City (cheapest diesel fuel in the country). It looks like you will not have the same range as we do. All our fuel is purchased at the Flying J's, and I use there website to keep track of prices. http://www.flyingj.com/fuel/diesel_CF.cfm
We stayed at the interstate rest areas and were never bothered. Like you, our typical stop was 6-7 hours, and we wanted to stop when I was tired, not when we reached an RV campground. The last run was Thanksgiving week and the rest areas filled quickly so we stopped and started early.
One rest area was so screwed up Patty had to go outside and blaze the trail for us to wind our way around the big-rigs. I think that was in New Mexico.
Tom, Patty, Hannah "The Big Dog" and Abby Kat, Indianapolis, Indiana 2000 36' FDS 72232 Our Photos
We live out in our old van. Travel all across this land. Drive until the city lights dissolve into a country sky, me and you - hand in hand.