I did a route in 2008 that mirrors your destinations. Deke Slayton Museum...I didnt think anyone would have that on their list too. I did part of it again in 2015
From Cody we went to Shell and over the Big Horns on 14..yes a big climb thru Granite Pass but great scenery. From Sheridan took 14/16 a lonely and scenic road to U Cross to Claremont (camping at General Store or near-by ranch) to Spotted Horse ( must stop) onto Gillette to Devils Monument ( worth it..nice roads as well). Went to Sundance and then Black Hills on Michelson mostly..and went east on 44 (Scenic is worth a stop) Entered Iowa on 9 and went east to Lake Okoboji and north to my hometown of Jackson MN and across the southern edge of MN ( Spam Museum in Austin worth the stop) to the Root River Rail Trail which led us to LaCrosse and the Three Rivers Trail to the LaCrosse River State Trail onto the Elroy- Sparta Trail. The tunnel is also a blast (without lights) The two museums will delight.
The 2008 trip was written up and can be seen at "Coast to Coast for Conservation" by Brad Edmondson @ FLLT.org web site and the 2015 trip at : https://www.crazyguyonabike.com/doc/?doc_id=15930
I am a huge fan of the Big Horns...especially that Granite Pass route from Shell.