indyfabz & johnsondasw - Your comments lead me to believe that the ACA maps suggested by Fred would round out many of my questions relating to overnights and supplies etc. From there, figuring out when I could jump an Amtrak home should allow me to flesh out a trip itinerary.
Yep. The maps show everything, including camping locations, grocery stores and motels. When you look at the maps, you will see that in WA it can be difficult to combine days shown on my itinerary. For example, to get from Winthrop to Republic instead of stopping in Tonasket would require a very long day with two passes. Same would be true if you stayed in Tonasket and tried to skip Republic.
The NT often follows the route of Amtrak's Empire Builder, especially east of Cut Bank. Go to Amtrak's web site, select stations and search by state. You will get a list of all stations in that state. Click on a station name to see if there is checked baggage service. The station must offer checked baggage service in order for you to be able to take your bike with you. East of Cut Bank, MT, Shelby and Havre have checked baggage service. I would also call ahead to make sure they have a bike box on hand.
If you find yourself pressed for time, at least try to make it into Glacier N.P. and ride the west side of Going to the Sun and maybe make the hike to the lake from Avalanche Campground. You could then double back to Whitefish for the train.