Although I have lived most of the past 30 years in Wyoming & Montana -
I did my grad work at K.U. in Lawrence and have done a great deal of cycling in Kansas.
One thing you did not mention was
when you are planning on riding.
That's an important consideration for comfort and safety.
I'll use climate data from Great Bend - smack in the middle of Kansas.
Kansas climate changes as you go from east to west.
Western Kansas in the summer is hotter, drier, windier . . . and emptier all year.
Eastern Kansas can be oppressively humid in the summer.
Kansas gets 60% of its precipitation in May, June, July & August. 3.5-4.0 inches per month.
Not to mention that the rain comes in huge storms of the Dorothy variety.
April, May & June are tornado season, but storms in Jul/Aug can be doozies, too.
September is the best month for dry conditions and more moderate temps.
https://www.usclimatedata.com/climate/great-bend/kansas/united-states/usks0232Because of the almost daily build-up of thunderstorms in summer, it is best to get your riding in early.
You can have a cloudless day at 7 a.m. and be dodging hail by 3 p.m.
Also, hot and humid afternoons in the east and 100F+ in the west make morning riding preferable.
Which suggests an east-to-west direction - not only to have the sun behind you and be more comfortable -
But also because riding early into the sun makes it more difficult for drivers to see you.
Finally, there is the wind. Wind is a reality that touring cyclists have to accept as a given.
You can plan and plan and plan to ride with the wind and still get headwinds.
In Kansas in the summer, the prevailing direction is SSE - (See wind rose)
A little more SE in east Kansas, due South in west Kansas.
https://mesonet.agron.iastate.edu/onsite/windrose/KS_ASOS/GBD/GBD_jul.pngNo matter where you are on the planet, winds tend to increase in the afternoon.
Caused by warming of the lower atmosphere.
Made worse in Kansas by the lack of trees to break the wind.
So, yet again, it pays to ride early.
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It may be only marginally better to ride east-to-west
Since the wind will be largely a side wind.
But the biggie is to start your days early.
I would suggest up at sunrise and on the road within the hour.
Just a snack and some water.
Then stop in a cafe mid-morning for a big breakfast.
It is a magical time to ride.