You said that AA had issued the ticket with AA flight numbers whilst the flight was operated by CX. But your routing was JFk-YVR-HKG. Does you ticket actually say JFK-YVR-HKG or just JFK-HKG. Because:
1) AA does not have authority to operate under AA flight number for JFK-YVR. If it's that AA would have booked it as CX. If your ticket was routed that way, you COULD have gotten out of YVR and was fully entitled to sit in First.

2) Yes, unfortunately if CX is to calculate your fare difference, it will stipulate the rules of the Oneworld RTW fare which is that there is no refund due if you are to travel in a lower class.

Yes it is not your fault. But unfortunately you chose to fly that day in Business Class because someone somewhere cancelled your reservation. If it is a CX operated and numbered flight, and AA reissued the ticket and did not queue the ticket number to CX, CX will cancel the booking. If the AA agent failed to note that, well, that is most likely what happened! If you had decided to accept travel the next day, then all would have been fine.

But I agree withnumber_6. It is not really the fault of CX that you got downgraded, but rather communications between AA and CX. I wouldn't drag your travel agent into this as he / she has nothing to do with it. However, it would have solved part of your problem had you asked AA to reissue you with OPEN dated tickets entirely and you asked your trvl agent in HK to book all your flights for you.

Basically you could ask your travel agent to forward your letter to the relevant departments. Or you may call CX res in HKG and ask them to give you the proper address to send a couriered letter to instead of just the PO Box.

I once was travelling on a full J class ticket. CX bumped me off on a confirmed reservation even though I checked in well ahead of my check in time. They didn't transfer me to another airline as my ticket permitted travel on whatever airline I chose. But they were apologetic and just gave me 2 one class upgrade for future use.