Currently, AA has 77Ws on 2x JFK-LHR, 1x DFW-LHR, 1x LAX-LHR. Come 2014, they will be adding a third 77W on JFK-LHR, and one on MIA-LHR.
By then, AA's refurbishment of its 772s to 2 class with fully lie flat J will be in progress.
OP: Upgrades using miles are usually very expensive (and usually not worth it). Does your employer allow you to pay the difference between Y and J to upgrade yourself?