OK everyone take a deep breath and count to 10, if I have learned anything over the years it is that Canadians and Americans have vastly different views on handguns. No amount of chatter on this Forum, or face to face will change those views, so please deal with the OP's original question, which is how to get the gun from Utah to Washington.
As for crossing the border, we all likely can cite more horror stories about crossing into the US as opposed to crossing into Canada, yet the fact remains, they all have a job to do, and take orders about what the flavour of the day happens to be. Each country has much to offer by way of sights, tourism, and reasons to visit, but remember we each are independent countries with our own laws that need to be respected. I keep telling myself that every time I have to swerve to avoid a collision with some idiot here in the USA who is driving down the highway at 70 +m MPH while texting.
Ed