May be common knowledge, but you can also use a 45k award on AA to get J on CX JFK-YVR. This also allows an open jaw and a stopover. FWIW, AA's availability mirrored asiamiles exactly for the dates we checked.

We were able to go JFK-YVR on CX and spice it up with Q(u)antas YVR-SFO, AS SFO-SAN stopover for the entire semester, and then go SAN-LAX-JFK on AA. AA tickets are extremeley changeable up to the last minute - as long as you avoid the $50/$100 fees for the advance purchase (assuming no EXP status).