Am I missing much if I skip Washington and start in Oregon? I would love to keep this around three weeks if possible.
Depends on who you ask and what you want to do. My short answer if you want to keep the route to three weeks and see as much of the actual Pacific Coast as possible, then yes, start in Oregon.
There are two "main" Coast Routes, the Peninsula and the Inland. The Peninsula route starts in the NE part of the Olympic Peninsula (Port Townsend/Angeles), heads west than south along the Olympic Peninsula. The Inland route goes through the Puget Sound region. Depending on whose Inland routing you use (either the Kirkendall/Spring Bicycling the Pacific Coast book or ACA's Pacific Coast Route), you can join up with the Peninsula route around Aberdeen (Kirkendall/Spring) or near Astoria (ACA).
The Peninsula Route to me is worth it if you can invest the time and energy into getting off the main road (US 101) and explore Olympic National Park. But these explorations mean side-trips anywhere from 10 to 40 miles round-trip to see things like the Hoh Rain Forest and Sol Duc Hot Springs. 101 itself stays inland north of Aberdeen so you'll see very little of the coast. South of Aberdeen 101 stays nearer to the coast.
While the inland routes go through some lovely countryside and you'll see quite a bit of the Puget Sound or Hood Canal (depending on the route), you don't see the actual ocean. But it is more direct than taking the Peninsula route.
What do you think your daily mileage will look like?