Thanks all.
gbkid - it's a ex-HKG ticket to another Asian destination..

That should be much much easier

I'm ok with the refund taking 6 weeks plus. I'm wondering what the minimum time to cancel and get the new ticket is. Can I do this, let's say within 3 days of the flight?

Try to do it as soon as you confirm a cheaper ticket, do keep in mind that Online Check-in starts 48hrs prior departure, this give them enough time to do pax management stuff, you don't want to keep two seats, you never know who really need that seat in the last minute, you still have to pay the "penalty"

This is through a travel agent - I wonder if they have any restrictions..?

Yeah, some agents doesn't like to deal with these with you, and give you all sort of reasons, airline not-allow, so difficult to call seat for you, because in the end they have to get on the phone and the computer to do all the dirty work for you. They Book, Cancel, then Book again for you. The time cost them the same, aka you are still buying just one ticket. check the fare rules!

Do travel agents get a cut of the fare - so, for them, there's no invcentive to cancel a more expensive ticket for a cheaper one..?

I am still not quite sure how this work now, but I know my TA's price is $20 extra then the price you see on CX website (HKG), but he can always get the flight and seat I need without asking, and If i go for HKG/TPE/HKG I can do a KA/CX mix, which give me better options in terms of time. I am sure they get something from the airline?
Cheers^