Another idea that someone else has noted is possibly taking a short flight to either SEA/SFO/LAX and taking a flight outbound on an asian carrier. From SFO/LAX there are routinely fares to Taiwan/Japan for about ~500-600 (600-750 all in). You can either drive to Seattle or find decent fares for about 150 all in from PDX to SFO/LAX. I'd personally wait until either mid Jan to Mid Feb for most of these fares. Just make sure you give yourself plenty of time for delays etc on the domestic portion.

If I remember correctly, China Airlines also flies to Seatac...at least I remember seeing an airplane there before.

I hope this helps.