Your UA options, in terms of not missing work, do not look promising. The best that I see is:

United Airlines 5876
Canadair Jet
3:50 pm Atlanta (ATL)
5:45 pm Washington (IAD)

United Airlines 177
Airbus A319
7:00 pm Washington (IAD)
9:23 pm Los Angeles (LAX)

United Airlines 839
Boeing 747-400
10:40 pm Los Angeles (LAX)
6:25 am (2nd day) Sydney (SYD)

I'd personally be inclined to take one of the later DL 767 nonstops (6:11 pm or 7:06 pm), and I probably firmly insist upon the re-route if you need to work a full day. If you can justify the need for an evening departure adequately, I'm optimistic that you will be able to find an agent who is willing to accommodate you, even if it means you have to try a few times. However, as zrs says, you might want to keep this option in your back pocket and see if furture changes make other options more attactive before playing your cards.