Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
You are, of course, free to include one BA partner on your award redemption between the U.S. and Europe for no additional mileage. So once June 29 rolls around (AA does not release reward seats until 331 days in advance), you could also check availability on the AA LAX-LHR nonstop, or BA availability from some other U.S. city (like SAN, LAS, PHX, SFO, ORD, JFK, IAD, BOS, DFW, MIA) with the connecting flight flown on AA. In fact, you could even have a free stopover at the connecting city if you like, as long as BA considers it to be on the "most direct route" between LAX and LHR.
AS from LAX to SEA or YVR, with BA from there to London, might also be possible. Not sure how far in advance AS opens up its award seats.