So, no offense, but I don't understand why you would try to force a tour into the wrong time of year. You will almost certainly encounter a lot of rain and cold, which is not just, you know, wet and cold, but can be kind of dangerous too, as drivers won't be able to see you as well, there's more debris on the road, you get more flat tires, and to top it all off a bunch of the camp grounds will probably closed, and you won't meet any other bike tourists like you normally would.
Depends on your point of view, I guess. I commute year round, so rain and cold are just part of the great outdoors for me. Aside from accepting those, I think there's a couple things you may be missing.
First, "starting in March" doesn't necessarily mean, "starting March 1." OP could, with the distance involved, start the last week in March, depending on mileage and stops. As I understand it, winter storm season in the PNW winds down sometime in March. A week or three where there's a risk (not a guarantee) of a storm hitting is a nowhere near planning to ride through three months of Aleutian Islands winter weather.
Second, the northwest coast is a rain forest. If you're going to avoid rain at all costs, you'll never ride from Washington (or north of the border) south to northern California. The best you can do is watch the weather forecast and be ready to take off for a week or two with minimal notice. Not many of us can do that, and stopping a bike ride there when rain is in the forecast is a good bet to break up the rhythm of a long tour.
One last point is that tourist season seems to pick up in the summer, when school's out. Spring and fall are often easier to deal with, traffic-wise, in touristy areas. OP can ride in the spring? What a great idea!