I second getting the QF account. Then download the KVS availability tool and use the QF credentials to see inventory.

Stick with it. I got QF/KVS to use miles for 2 tix to Vietnam a couple of years ago. T-2 days before the trip, my outbound itinerary was:

SFO-JFK AA F
JFK-NRT AA F
NRT-SGN JL J

Continuing to hope for CX award inventory, my T-1 day outbound itinerary then became:

SFO-HKG CX F
(18 hours to see HKG)
HKG-SGN CX J

Good luck!