Most of the overseas airlines will not upgrade offline non-revs into business class, particularly the large ones (in fact some do not even let their own employees sit up front such as Emirates).
Qantas is likely to be on your itinerary, and they do not -- but their coach product is obviously way better than any US carrier, so at least you'll have decent food and good entertainment options and more polite, friendly employees from the ticket counter to the moment you get off the airplane.
If your plan is to go to Australia, there are a few options depending on if you are traveling there alone or with someone else. If you want to save some money, you could try to jumpseat there on Delta or United. You'd pay nothing at all for the southbound leg out of LAX or SFO. United is great about upgrading jumpseaters to business class, too -- if there is a seat open. They actually apologized to me once for only having economy plus.
I took Qantas on LAX-SYD after not getting on United and it was $120 at the time so your total round trip estimate sounds just right.
Coming home, once you're back from Perth to eastern Australia, you could try to take a US carrier home too -- this would save you the bulk of what is in the ZED pass and you'd just pay the Australian departure tax at the Delta/United/Hawaiian ticket counter.
If it's still like it was last time I looked, you'd actually be able to try Delta first thing in the morning leaving SYD, and then if you didn't make it, you'd have two attempts on United, one to SFO and one to LAX. When I had come up on the United MEL-SYD segment, they said if I didn't get on LAX they'd still be able to send me over to the SFO gate which is right next door. I ended up getting business class to LAX though so it worked out.
Hawaiian is an option on SYD-HNL as a jumpseater if you could get back to Texas with little hassle from HNL.
Air Canada is also an option with SYD-YVR. I would just not make them at the top of your list because if none of the pilots have the little paper jumpseater booklet thing, then you're not going to be able to go with them.
You mentioned you haven't done a whole lot of international non-revving so I will just say that the domestic traveling abroad such as intra-Australia or within Asia etc. is generally much easier than the insanity you can come across at a hub in the USA on a Sunday afternoon. There aren't hordes of non-revs trying to get home or get to work, or a dozen buddy passes, and so on. From eastern Australia to Perth I wouldn't be surprised if you were the only non-rev in both directions.
