For what it is worth, I took the following route going the other direction in 2016:
Yellowstone - Togwotee Pass - Dubois; reasonable cycling
Dubois - Lander; not a huge amount of traffic, otherwise fine
Lander - Jeffrey City - Rawlins; Adventure Cycling Route, windy when I went
Rawlins - Medicine Bow - Laramie - Went to Laramie to facilitate side trip to Front Range
Laramie - Walden; a few narrow stretches but otherwise fine
Walden - Kremmling; sometimes busy but otherwise fine
Kremmling - Copper Mountain; Summit county busy at times but also some separate bike routes
Copper Mountain - Leadville; snow on the summit but reasonable pass
Leadville - Salida - Great Sand Dunes Pool - Sand Dunes themselves interesting but I'd been there before; nice hot springs.
Great Sand Dunes Pool - Antonito; larger highways but ok shoulders
Antonito - Taos; few sections of narrow road with a lot of traffic