"Jes shoot 'em."
I have toured in nearly every state in the U.S. and province in Canada.
I can assure you that there is a correlation between how far south you are and how many dogs you have to deal with.
I ridden cross-country 6 times and bunches of other multi-thousands mile trips mostly in the West.
I prefer the rural West for the reasons you give - easier riding, simple and nice and free camping.
I've never taken the TransAm all the way, but have covered most parts of it over the years.
There's no reason you can't do your own routing - it just takes a little more effort and planning.
The ACA maps for the TransAm and other routes are very helpful -
Plus you'll bump into more riders and have more services if you stay on route.
The Midwest should be O.K. temperature-wise in late May with far fewer dogs and coal trucks.
I think riding across Nebraska is more scenic and cooler than Kansas by 5 or more degrees.
(You'll have winds no matter where you are in the Great Plains - they are, after all, the plains.)
If you are riding via Nebraska, you might consider riding over two gorgeous mountain ranges in Wyoming.
From Laramie you can head west and have the jaw-dropping vistas at the top of the Snowy Range.
Then continue on from Riverside over the Sierra Madre to Baggs on a magically empty road.
(Or from Riverside you can join up with the TransAm route via Rawlins.)
Do I have a pic of Medicine Bow Peak in the Snowy Range??