I'm not sure there's a better way, although awardnexus.com might be a better interface to BA.com availability, although there are some usage limitations/costs.

Generally I find that if CX shows 2 or more seats via AsiaMiles, then you should be able to get at least one via AA. If CX only has one, then it's a crapshoot.

I was recently very frustrated trying to change to a HKG-JFK nonstop (the YVR 1-stop) on the day of departure, even though CX had 1 Z seat open. The Airport Express agents couldn't even change me within the check-in window. At least I got more time in CX F.