Sorry to post and disappear. We just moved to a new city and it was more work than I thought getting settled.
Thank you all for the great advice. I have made a few calls with this information and the CSRs have taught me a lot as well. I am trying to take a trip to Australia at the end of June. Here's some tidbits:
British Air & ANA: Could not get through, was on hold forever.
Air Canada: Got through right away both times I called. First CSR was very helpful telling me how everything works. She was able to find business bookings quickly over a month between N. America and Australia. The problem was there were very few direct flights (she found 1), apparently these bookings get eaten up a year in advance. Working with her and playing online makes it appear that Aeroplane's site has everything listed already. She was unable to give me something I couldn't find myself on their site.
United: Similar to Air Canada. Helpful, but not getting me any flights I couldn't get online. I was able to learn that the leg I want most has a lot of award availability and I can wait for a short leg to pop up before booking. If I book now there will be a 7h layover in LAX. I may book the flight anyway to lock in the main leg and hope to change the first leg later.
Your advice coupled with the CSR help and the act of doing all of this has made me much more confident searching out and booking flights. Through this I was able to find 3 direct flights to Eastern Australia from Vancouver which are very rare. I booked one of them! The other 2 I was going to suggest here have already been snatched up. Everything changes quickly.
Lastly. I reached out to an award booking site that helps you find flights. I was able to email back and forth a bit with them about my itinerary. Their cost was $300 if I wanted them to take over. After doing all this I would say they are not worth it for me. I thought they would have some tricks that would get me on the best flights, but they're playing by the same rules. I'm sure they are experienced and creative, but after giving them the details of what I had found it didn't look like they could do any better.