Most of my miles are with BA, also some with AA. Searching for awards on other OW carriers seems unduly difficult. I'm looking for 2 business or first tickets from NYC to SYD next Feb. A search on BA shows availability in Qantas Y class via LAX (why does this come up when I'm specifically searching for C or F?) but no mention, for example, of CX via HKG which would actually be my preferred route, nor any other partner airlines.

Does anyone have any suggestions for a detailed online search? I know I can call BA but I find them very user unfriendly on the phone ... and there is usually a long hold time. Thanks.