The FAQ says nothing about whether the 773s flying LAX-HKG have been converted. In fact, it says that there are no 773s flying that route. And my confirmation says that the plane is a 773, not a 77A. So, the issue was not addressed.
CX's 777-300 is a regional setup and does not have the leg to do LAX-HKG non-stop. The only CX fleets that can do LAX-HKG non-stop are 744, 77W(77A), and 343 (with heavy payload restriction.) So one would pretty much only see 744 or 77W(77A) in LAX (and in fact, CX will convert all 744 LAX flights into 77W(77A) in mid-December.) In your case, 77W(77A) for sure.
All the 744s and 77Ws have the new lie-flat J seats.
AA's website probably just doesn't care to distinguish the 773 or 773ER(77W/77A).
Enjoy the flight!