There's a reasonable amount of availability. The following itinerary is available:
23/10 BNE-HKG CX156 00:55-07:45 (J)
23/10 HKG-LAX CX898 09:30-07:55 (J or F)
13/11 LAX-HKG CX897 08:35-16:15 +1 (J)
15/11 HKG-BNE CX157 12:35-23:20 (J)
You have to do a mini-stop in HKG on the way home although...