A follow up to my post above. I called back today to see if I could book another ticket on my same itin (LAX-NAN-AUK, AUK-SYD-NAN-LAX). They had availability in coach on the outbound and biz on the return. So that's three AA awards on Air Fiji on the same flights and routing!
Earlier I was unable to book the DEN-LAX portion as Air Fiji did not publish a fare. Well, the agent today asked me if I wanted to add the US domestic portion. So no I've got that added to all three tickets. Not sure what happened there and am so glad something did so I don't have to buy the domestic hops.
All in all, I've heard that US-NZ is almost impossible to book. I've had a great experience and feel really lucky! Now if only AA allowed a stopover in NAN!