Here are cycling maps for both states:
Nebraska - http://www.transportation.nebraska.gov/docs/bicycle-guide-current-2.pdf
I've ridden across Nebraska many times - way better than Kansas.
Too many people stay on US 30 or US 6/34 - - bleah!
Doable if you are in a hurry and just want to cover the miles.
Hwy 92 from Arthur to Broken Bow lets you see the Plains as they were 200 years ago.
Much of the Sandhills region has never been plowed up. Very light traffic.
Little towns every 30 miles or so - much easier than Western Express.
It's a stormy time of year and you'll need to use caution.
There are some wonderful county roads across the southern tier of Iowa -
But you indicate you want to hit Des Moines.
If you cross the Missouri at Plattsmouth,
you can zig on county roads up to Silver City and Griswold.
Traffic on Hwy 92 drops considerably east of Griswold to Winterset.
Then zig-zag to Cummings and take the rail trail into DM.
Back roads via Montezuma to Iowa City.
Very few roads in Iowa have shoulders - be careful -
Choose routes with as low of traffic as possible.
Iowa is very bike-friendly - but the roads aren't great.
Pic - Loup River in Nebraska