Can't speak too much about SEA-TAC strategies, but I'm sure you'll have to change planes at least once! Try to avoid any that change at London, because of the British Air Passenger Duty on the way home, and the huge hassle of Heathrow.
I did a little random searching for next July, using an open-jaw plan: Fly to Lisbon, train to Porto, fly to Barcelona, fly home, and found fares around $1600 on offer. Lisbon is not that competitive a city, so one strategy would be to keep an eye out for sales. If you can snag a cheap roundtrip to Barcelona, $150 will buy you BCN-to-Lisbon and Porto-to-BCN for the middle part. The main carriers on those routes are TAP, Iberia and Vueling.