I would suggest you continue on the TransAm route to just inside Kansas, say Tribune or Scott City. From there you can take almost any state highway as very little traffic tends to travel on them as there are not that many people in these states. You can go to http://www.ksdot.org/burrail/bike/pdf/bikemap2006.pdf
and it lists Kansas' traffic counts and road widths. Nebraska and the Dakotas may have something similar.
Nebraska and South Dakota should be the same or better as even less people travel there. I drove Highway US83 in 2001 and it was fairly lightly traffic.
I believe there is a rail trail that goes halfway across Nebraska or one of the Dakotas. Do a rail trail search and you should be able to find it.
I really wouldn't worry so long as you stay off the interstates or any 4 lane highway. Obviously, you can reconnect to the Northern Tier around the North Dakota/Minnesota border and follow the maps in.
If you time/route permit it you should head due north to the Black Hills area of South Dakota. The area is really nice. No matter what, you should hopefully get some nice tailwinds heading northwest.
Hope this helps!
Happy trails and may the wind be at your back!