When you get into Washington, I'd recommend heading a bit further north from US 2 and pick up SR-20 through Winthrop. IMO, it's a better road than US2, wider and less twisty and I think the scenery is better - more open vistas rather then the "down in the gorge" feel of US2. It does climb higher (5200 ft compared to 4200), but the traffic is less. The State Highway Dept. has done a lot of work on it in the last four years or so.
It's usually closed by snowdrifts by late November - too much work to keep it plowed, but in September it should be great.