Next time ask for the confirmation numbers with the other airlines when you are still on the phone, they have them when it gets ticketed.
It's becoming a pain to get a trip overview now more and more airlines don't display on sites like checkmytrip anymore, but you need the PNR's for your seat reservations anyway.
A good agent will offer them them you, but most don't :-)
CX availability in Asia is fairly restricted even though there's plenty of flights. Couldn't get anything either for HKG-BKK/KIX/DAD when I was trying for my dates, just others....