You would be splitting the journey into several segments. So instead of search LHR to SYD you look for LHR to HKG. Then separately HKG to SYD. The companion voucher adds a complication to this but plenty of TwoFers have made it to SYD. If you are seriously into Avios availability issues consider joining AwardNexus or KVS, which show things more easily, though personally I don't use them.

A few little odd ones to look out for are, for example, Royal Jordanian's flights to HKG, BKK and KUL, though they don't run it daily. Also linking in with Cathay via places like CMB and the rest of the Indian sub continent.

Also bear in mind that it may make sense to book an Avios trip to somewhere near by, and then cancel if the last minute availability opens up.