The basic issue is that AA did not change anything. CX changed its schedule and you are being offered the next available flight with award space. CX can't be forced to do anything by either you or by AA.

Calling AA back is useless on the CX front as you have already had the Liaison Agent (or Desk) call CX and CX has said no.

But, what you can do as others have suggested is do some research as to other OW routings from your origin to BKK and check availability on those. AA will force space for you on its own metal, but can't force it elsewhere.

Having the research in hand, e.g., dates and flight #'s will be very helpful.

Beyond that, your options really are to lump it for 14 hours at HKG (day rooms?) or to cancel for a refund (to which you are entitled).