I second the recommendation of CX at HKG airport - they have now done three reissues for me, taking between 15 & 45 mins depending on complexity. But for me at least (as a Diamond) I have been able to proceed through to The Wing (on a temporary boarding pass if I needed the ticket for the flight I was about to take) and someone has brought the ticket through for me there. (This of course requires you to trust the ticket counter to get it right, but they have always done so for me.)

I would not recommend the CX City ticket office, at least not the AA desk there who recently took over 90 mins to do a reissue for me.

(Most of the tickets I have had reissued by CX have been from AA/Emeco in Cairo; one was from CX Paris.)