Pickles, I am going to go against the grain and say that they shouldn't offer you compensation for the simple fact that I don't believe they did anything wrong. Here's why. Reservation problem aside, you voluntarily gave up your seat from Vancouver to Hong Kong. Doesn't matter if they didn't tell you or you had to ask. Bottom line is that there was a seat available, it was offered to you, and you voluntarily declined it. So I don't think they should compensate for a voluntary downgrade under any circumstances. The New York flight is a bit stickier, and I think that's where the ticketing issue came in. Whether they could put you on the New York flight really just depends on their system, which I dont know well enough. But it seems to me that if you have a JFK-HKG segment and they wanted to bust it up in order to get you basically JFK-YVR-HKG due to the necessity of different boarding passes and therefore different flight segments, it would necessitate a reroute. Something that no one could hardly expect them to do on short notice (though an AONE3 wouldn't be that hard). Additionally, they run the risk of you deciding that you just dont want to move in Vancouver and causing a scene. I disagree with GB about compensation for the downgrade, though. There is nothing in the rules that says that if you are to travel in a lower class that there is no refund. What the rules do say is that if inventory is not available when the booking is made and you have to fly in a lower class that there is no refund. In your case, the inventory was available and you had a valid reservation and you had to fly in a lower class and therefore it was an involuntary downgrade. There is a subtle difference and obviously it's debatable, but that clause doesn't give license to an airline to involuntarily downgrade a OWE pax if the cabin is oversold without paying compensation.
FWIW, I don't think your beef is with Cathay. It's with American for mucking up your reservation and for not knowing the procedures well enough to make sure things went without a hitch. Not an uncommon problem. Cathay is fair and Cathay will take responsibility for things that they create. But they are far more reticent to take responsibility for things either that are out of their control, that they did not cause, or that aren't actually problems.
This isnt the same situation as TrvlGuru and I think if you pushed it to the same degree with CX as he did with BA that you would lose. Sorry.

And for what it's worth again, you got screwed. And frankly, I dont think you will get AA to fess up to anything, so if CX says no then I think you will be screwed again. The difference between one-way F and J between JFK and YVR is about $650. If Cathay offers anything remotely close to that, I think you should take it, move on, and like many of us learn from it that there are several OW carriers that you can't trust to always do things right and that it's prudent to check up on reservations with the other carriers.