Some update on my experience, I called a second time (queue is much longer in the middle of the day than in the morning) and this time the agent was able to help me book the Nadi -> Auckland leg without issues, plus some new taxes and fees for this new leg. This was without needing to be transferred to the partner desk.

One interesting thing, I am actually traveling IAD -> SEA -> SFO during the domestic portion all in the same reservation. There are direct flights from IAD -> SFO, but it seems like if I am booking the award as a partner flight with Fiji Airways I need to go through Seattle even though there is availability in the IAD -> SFO flight. Not sure why, but it's not so bad.

Thanks everyone!