In reply to Captain Gear:
It's a long time since I worked in the travel trade, but my gut feeling is yes you can get better, possibly under a grand. I'm sure that some of the American carriers will offer a LON-BUE return via the states, and for a premium you may even get the California stop-off as part of the ticket.
But you wont get the best prices online for this sort of complex itinerary. Piecing together multi-stop journeys and keeping them within fare guidelines always used to be a real dark art, and possibly still is. A good travel agent with a thorough knowledge of fare structures is far more likely to spot the big savings than a computer is.
Like I say, it's been a while, and I'm not sure who the leaders are now, but I'd guess that there are S. American specialists who will be accustomed to the sort of requests you're making. My advice is to pick up the phone and be prepared to wait while the agent sifts through the possibilities. Too quick a response means they haven't considered everything, but if they are clearly struggling end the call.
Good luck. I'll be genuinely interested to hear how you get on!