Thanks for replying - I'm clear about why using a TA would solve this. I would assume that there is no way a TA can now take over the booking which CX has made?

I can't understand why CX can't add a sector to the existing PNR for the TPE-HKG sector on the existing PNR, the return flights are wide open, so I would make the return flights on the same booking as well then just give them my ticket number. Are there any magic words I can say to CX to get them to do this? If I was able to make a booking from HKG-LAX, surely I should be able to add flights to this booking?

Alternatively, do you know if there is a way to get them to extend the deadline so i can fly early on the 5th to Taipei and try winging it with the checkin desk to use my booking for the flight and go standby TPE-HKG?

There must be some solution - I really must get to LAX on the 5th, but there are absolutely no seats on any class on CX.