Well, the TransAm route to Alexander is all paved roads (although the expansion joints in eastern Colorado may stretch the definition of "paved"!). Unless you're getting off onto the county roads, meaning you have lots of very fine maps, I'd expect you'd be riding mostly U.S. or state roads north from Alexander -- no problem.
The farm access roads in southern Kansas are pretty good for dirt roads. I drove one afternoon to pick up our host from his haying job, and my Appalachian roots had me gritting my teeth as I drove up to 40 or 45 mph on the dirt roads. He had me drive home, and told me I could really be driving 60. I just couldn't do it -- they're DIRT roads, after all!
Two things I'd be cautious of: first, is there a creek or river that disrupts the back road / county road network. Second, Alexander, KS is only a town on AC maps. Don't count on anything but water there!