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
If it were me... Spokane to Sandpoint would be SR 290 (WA) Idaho 53, 41, 54, 95. Actually beeter would be Centennial Trail to Post falls then north to 53. Just last weekend I rode the centennial trail from Spokane Valley to Post Falls and back.
Link to the Milwaukee RRhttps://lh4.googleusercontent.com/-O...system-map.jpg
In Washington it iron Horse State park west to the Columbia then it is the john Wayne Trail. The map shows spur lines to Spokane and Cd'A Id. however I'm faily certain that the rails to trails Fish Lake trail out of Spokane does not exactly connect. Something to research further.
The John Wayne Pioneer Trail east of the Columbia is an adventure in itself. 4" tires and a Surly Long Haul Trucker seem to work on the ballast. The services are few and far between. Just finding water can be an issue.
This chap did it and produced a very informative account. I'd do it with a fully equipped sag wagon and bike shop.
Arlington, over Cascade Pass and on to Spokane, then onto the Centennial Trail there sounds better. Then you connect to the North Idaho Centennial Trail, work over to the Trail of the Coeur d'Alenes and on to Montana. There are a number of good trails in the Spokane - Silver Valley area. The TCdA is a tourist attraction.
26InchSlicks: Crossing Washington State On The John Wayne Pioneer Trail