Hmmm... I'm not aware of any big show in Washington. There are a number of shows out west which you could travel to. The Draconic Awards run the painting competition at a number of shows out west. The biggest is the Las Vegas Open in February. Then there's Kublacon in Oakland in May. Califaux is in Sacramento, CA in June. While the tournament there is Malifaux, but the painting competition is open to miniatures from any range. And the Bay Area Open is in San Jose CA in July. They've got some nice prizes (typically an airbrush for first place), some painting seminars, and I think all of those except perhaps Califaux are also Crystal Brush Qualifiers.
Those shows are all tied into gaming competitions. In terms of a pure miniature show/competition, there is the SCAHMS show in LA in April. You'll get a mix of historical as well as fantasy and sci-fi figures there.
Unfortunately all of those are going to be either a crazy long drive, or a plane flight away from you. There may be more going on in Seattle (or up in Vancouver or down in Portland) that I'm just not aware of. Check for gaming competitions as many of them will have figure painting contests as well. If you're going to check out any of the ones I mentioned, I'd think the Las Vegas Open (
https://www.frontlinegaming.org/las-vegas-open-2016/) would be the most worth the trip.