It would be a great deal easier if QF had a flight exPer at 0900 or earlier instead of 1230..... (They did at one time) Or if CX had a slightly later flight SIN-HKG
I can't help to think that QF do not want you to be able to use that connection. Even though there are some fares HKG-PER that allow the SIN connection. At this point I would jump to the first one that code shared PER-HKG with AA for connections HKG-USA or PER-NRT with AA.
Fred
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