Welcome to FT!
If your earning preference is with BA it might also be worth looking into K-UP and Y-Up fares that originate in LAX. This would require you to initially book a one-way ticket so to avoid nesting but generally from what I've been able to see fares are cheaper starting west. Have a look at this thread for more info:
http://www.flyertalk.com/forum/briti...-point-76.html starting at post 1126