If CX non-stop to HKG is not available, try:
LAX or SFO-(JL)-NRT-(JL or CX)-HKG-(CX)-DPS or CGK.

JL and CX combined have several flights a day between NRT and HKG.

CX has two flights a day from HKG to CGK as opposed to JL with only one flight from NRT to CGK. If you have to fly to CGK, there are a lot of domestic flights to DPS.

Hopefully this will help with the availability.

As a last resort, if there is absolutely no availability on JL to NRT, you could take AA to NRT. Of course it is not JL or CX quality, but it'll get you there with your miles.