I am familiar with warm showers and will look into that. The problem there lies with my wife who is not so keen on "strangers" in her house. Then again, where we live does not lend itself to many overnight tourists so...... Worth considering for my benefit.
I think the suggestion was to use it for places to stay, not for you hosting others. You don't have to host in order to be a guest.
As for hotels/motels, you will likely need to make advance reservations in Glacier National Park and its environs (e.g., Columbia Falls, Whitefish) and Waterton Village if you do the western Canadian portion. Another problem spot could be in the area of the North Cascades National Park. IIRC, there are limited options from Mazama west to maybe Concrete. There are places after you descend from the pases, but I think their size is limited so there may be competition for space if you are there during high season.
If you find you can pack them, a light sleeping bag and/or mattress would give you the option of staying in campground cabins, such as those at the KOA in Winthrop, WA and the Adirondack shelters at Steelhead Park in Rockport, WA.
BTW...The NT is sufficently south of Chi that you are not influenced by it. In fact, the portion through IL was pretty rural much of the way.