Other options could be Virgin Australia... flat beds in business class, but again two connections. Also the same with delta, flat beds again, but connect in lax and sydney.
Otherwise, could use someone like Cathay... ord-hkg-per (just check to make sure its not a regional aircraft operating the HKG-PER sector, that only has recliners, but I think they have gone to all flat bed now), or even something like AA to NRT/HKG and then connecting with Qantas or Cathay from those ports to Perth.
If you provide some more details as mentioned above - class of service, any alliances etc, then this might help us to give more options. Getting one world top tier could be good if flying Cathay pacific. Very nice first class lounge in Hong Kong.
Redemption levels though AA are very good. Could get top tier (and access First lounges) and good redemptions.
Let us know
And welcome to FT.