Ok -- I have been trying to figure this out also from NY. You are right, the AA is easy. I did not think about the Canadian code on British. My thoughts were going AA to London, London to Mardrid on British, return on Iberia, back on AA. Then do a Canadia trip and Cathay from JFK to Vancouver.
Total cost was around 1500. $400 on AA, $450 LHD-MAD-LHR, $200 Canadian, $450 Cathay.
I can cut about $200 off the fare if I do NYC-Toronto (Canadian), Toronto-LHR(British), LHR-Madrid (Iberia), LHR-Toronto (British), Toronto - LGA (Canadian), JFK-Vancouver (Cathay).
Thoughts?
--Jim