Arizona Trail northbound, then continue north through Utah, Idaho, then cut west from Coeur d'Alene to Seattle. Almost entirely on unpaved roads, a la Great Divide.
Biggest hangup is crossing the Grand Canyon. From what I understand, those doing the Arizona Trail have to strap their bikes to a hiking backpack and carry them across. My question is where does the hiking backpack come from? Do you mail it to yourself, or do you carry it the entire time?