Breaking fares is beyond me but other options:
1) Buy separate tickets PUW-GEG. Would add ~$400 but much less than PUW-LON, and could drive if IRROPs seemed likely. Two one ways for maximum flexibility.
1a) Seperate tickets PUW-SEA, cheaper still but royally screwed with IRROPs.
2) Book different carrier FI/AS for instance.
3) Email BA and ask them to forward a request to their Revenue Management department to file a fare to PUW. Total longshot but if you don't ask.... Related, if you could find their local NA sales exec (like on LinkedIn) and send a message to them as well.