You need to get some planning software to run during the excursion. You also need at least the Western Mountain Directory - Might as well buy both while you are at it.
Run the planning software for a route and then plot it in the mountain books and see what gets a yellow triangle. If you are using Street Atlas, you can mark those roads as no good.
Going into Yellowstone from the east will take you over Bighorn. That might not wash, but you can by-pass that by going into Montana and entering the park from the north.
You can do this, but most of the western states are not as flat as Ohio.
Matt