Don't like surprises or research? Use the ACA maps. They'll very likely save you as much as they cost, keep you off most of the more dangerous roads, reveal needed service locations, and educate you about local interest spots and history. They now include elevation profiles.

Or for DIY, order states maps online. They're free, compact, and adequately detailed for a bicycle tour, with a bit of experience. Rough out your route with Google Maps, then transfer to the state maps. You can use satellite/street views to zero in on questionable sections. Better yet, contact Warmshowers hosts along the route for their advice about specific routes through their areas, and maybe a place to overnight. Great resource.

A couple of 3 day mini tours should get you ready for this expedition.