Your best bet is to do LAX-HKG-DPS as a one way award on CX and then pick up a cheap ticket to Singapore and you will have better luck getting a one way JL award SIN-NRT-LAX.
Do it as two one way single partner awards. We booked LAX-HKG-DPS and then SGN-HKG-LAX, using SQ miles for the DPS-SIN-SGN segments.