My advice is to start playing with route options on Ride-with-GPS!
There are numerous combinations and you can choose what you like best regarding distance, elevation gain, maximum gradients, remoteness, etc.
E.g. you can exit NE of Ketchum on the Trail Creek Pass Rd which is dirt and has a very good surface.
From Chilly you can go NW to Challis or NE over the Doublesprings Pass or SE to Mackay and further NE over the Pass Creek Summit.
In the Lost River Valley you can go NW towards Ellis or cross the Lemhi Range on the steep Big Windy Peak.
You can enter Montana from Leodore on the mild Railroad Canyon Rd over Bannack Pass or from Tendoy on the Lewis and Clark trail over the steep Lemhi Pass.
Use satellite view and streetview to inspect road surfaces and find services.
Here is just one proposal :
https://ridewithgps.com/routes/29110483