"Here's my route (first draft) based on AAA maps to get me from Muscatine to Manhattan:
In Iowa:
S. and W. on Rt. 92
To S. on Rt. 1
To W. on Rt. 2
Turn south at Centerville on Rt. 5 to enter Missouri."
I've ridden most of the roads you list above. Highway 2 in the mid 1980s was OK for bikes. Now, you likely won't get killed on Highway 2, but it has plenty of traffic. The section of Highway 1 you list from above Washington to below Keosauqua is heavily traveled except for the last 15 miles or so. Highway 92 also has plenty of traffic. I would not choose your route to get from Muscatine to Manahattan Kansas. At least not the part in Iowa. The part of the state you are biking through in Iowa is rolling hills and plenty of turns in the roads and plenty of trees. So visibility of cyclists by speeding cars may not be that great. Best to stay off high traffic roads like 92, 1, 2.
Get a state map, a real paper map, not the less detailed Rand McNally. Pick out any of the more rural roads and you will be fine. Stay off the main Highways like 92, 1, 2, 34. Of course that kind of leaves you with not many roads going west across Iowa since it seems only the main highways go straight west-east across the state. Can't really give you a recommendation of which roads to take, just the ones not to take.