Note: after labor Day, some stuff starts closing. Just something to be aware of.
The TransAm - there's quite nothing like it. The history of the country...and the history of the route itself. Services. The other cycletourists.
Okay, with that out of the way, just a random thought. Does it have to be the Trans Am? You could ride the eastern Trans Am and then pick up the Route 66 or even drop down to the Southern Tier.
Riddle me this, fellow forum denizens: raise your hand if you know why the Trans Am takes a ~400 mile detour north to Missoula. Anyone? Bueller? Bueller?