As mentioned above, finding three J award seats on the same flight from HKG to the US can be rather tough.

AA miles: AA, JL and CX are the only cost-efficient options

DL miles: several Chinese airlines ost people don't find too exciting; could try TPE-based China Airlines

UA miles: plenty of partner airlines and routing rules are quite flexible. How about NH via NRT, LH via FRA/MUC, LX via ZRH, OS via VIE, AC via YVR/YYZ/YUL?