Interesting you should choose this route because I have researched it and hope to do it someday in reverse. Born and raised in Everett, WA. US2 begins at I-5 in Everett and continues east to St. Ignace in upper MI. It starts up again in Burlington, VT and continues to Houlton, Maine on the New Brunswick border.
My US2 experience is from Everett to Sandpoint, ID.
Heading west on this route is beautiful, one of my favorite routes across WA. You can take it to its terminus in Everett, then I-5 north to Burlington, WA-20 west to the Coupeville ferry on Whidbey Island to Pt. Townsend. Pickup US-101 west through Port Angeles and then WA-112 west all the way to Neah Bay. A good place to camp here is Salt Creek County Park and take day trips out to Neah Bay.
Salt Creek Park also gives you good access to the northern part of Olympic NP: Hurricane Ridge, Lake Crescent, Sol Duc Hotsprings, Dungeness Spit, etc.
Another beautiful route across WA is to pickup WA-20 from US-2 at Newport, WA on the Idaho border north of Spokane and take it all the way across WA to Burlington where you will continue the route I described above to Whidbey Island and the Coupeville Ferry. This route crosses through North Cascades NP, The American Alps. Simply beautiful east to west.
Either of these routes passes through rural America and avoids the Everett to Olympia Puget Sound juggernaut on I-5. I believe you can accomplish any of these routes in your long timeframe. You are in for a cool adventure.