There is relatively little competition in the US-Oz market. Namely, only United, Qantas, and Air New Zealand fly there directly, which results in high fares.
Some strategies for getting there cheaper include going the long way:
US - Europe
Europe - Oz
In your case, you can fly DL or AF to CDG and then AF CDG-SYD. It's sometimes even less if you fly to LHR, then LHR on, but if you want to stay with SkyTeam, that may be difficult.
Doing it this way also allows you a stop in the intermediate city if you buy them as separate tickets.
The other way, which you touched on, is via SIN. LHR-SYD is too far for a 747-400, so many carriers stop in SIN. This results in an excess capacity of QF, BA, and SQ seats SIN-SYD.
http://www.flightcentre.com.au/ is a large Australian consolidator. Not sure if you can buy US-originating tickets there, but you can inquire (or enquire, since they're Australian).
Edited to add - Flight Centre does allow US bookings. Click "not an Austrlian resident" at the top of the website, and you get a country choice for US, and a wesbite with a toll-free number featuring a LAX-SYD RT for $875.
[This message has been edited by channa (edited 01-08-2003).]