You can mail your long guns to yourself care-of someone at your new location. That person is not allowed to open them.
When we moved many years ago we carried handguns on our Alaska Airline flights. We did not take possession of our baggage in Washington. This may be a real consideration with the current laws in Washington state.
You can also have loaded ammo in your baggage with certain limits on weight and packaging.
In past years going through Canada you were permitted to have 200 rounds of loaded ammo per person without paying duty.
You'll certainly want to verify all this but I don't things have changed except for , perhaps, Washington state laws
