If you have seen this blog it might interest you. It involves rails to trails, great photos, and a little history about trains. The guy who wrote the articles likes trains too. This particular trip might be too much given you longer journey.
On another point if you travel on Hwy 20 you will practically end up in Sandpoint.
If arrive in Spokane the trip to Sandpoint is possible there are a couple of options depending where you start from.
If you want to go east on I90 here is my recommendation for going into MT. I'm not sure what it is like once you get into MT, it isn't as direct as from Sandpoint.
idaho-montana day 6 in Thompson Falls, MT | MapMyRide