... and the short answer to the other part of your question is that when you have called up the results using the BA miles search engine, in the left column there is a box marked "Partner Airlines". You can widen the search to include OneWorld carriers.

The problem with YVR however, as others have noted, is that AA do not serve the route from LAX/SFO other than as a codeshare with AS. You can redeem BA miles on AS, but it is not part of OneWorld and so I fear it could not be combined with the SFO/LAX-SYD sector (i.e. it is not eligible to be included on a OneWorld award).

I would ring BA and see what the parameters are. You might have to buy the YVR-SFO/LAX sector and then ticket the SFO/LAX-SYD as a redemption. At least booking that would be simpler.

If you don't mind a slight detour, JL and CX both serve YVR and (subject to availability) could be used on a OneWorld award.