It is well worth the time to call the award desk and work through the options. It was also helpful to have some alternate dates and flight combinations written down in advance of calling, as I recently found when booking two F tickets on BA from SEA - CDG, FCO - SEA.

As far as connecting through other cities as the direct SEA-LHR (and reverse) may be full, take note that flying non-west coast (ORD, MCO, MIA, EWR, etc.) cities to get back from LHR will add a significant amount of extra time to the trip due to the flight routes. Going to YVR or PDX may be the best option despite flying on a Q400 vs. 737, etc.

Have a great trip!