You can also watch the BA boards for BA's regular sales from Europe to the US and book AA metal via BA. Or you can book AA directly during the BA sales since they always seem to have the same fares as BA.

Agree with dciolli that you want to try the 77W from LHR to LAX or go via JFK on the 77W (though I think they are down to one flight a day with that plane) and then transcon on the A321T.