It's really not a RTW you're talking about but a protracted one-way trip from the UK to Oz.

If it were me, I'd look at this instead -

Get to Oz as quickly/cheaply/comfortably as you can (note mutually exclusive terms, but maybe a World Traveler Plus or similar ticket could work.)

Once in Oz (even before your cargo has arrived on the boat) purchase a Circle Pacific fare in business or coach as your budget permits. Then you can do the S. America - N. America tour, returning via Asia. Given the Oz origination price for the CircPac fare, my hunch is that you'll end up money ahead and won't need to worry about incomplete RTW itineraries.

At the moment, you can't go to Fiji using either the RTW or the Circle fare, as Qantas don't operate their own planes there. But living at BNE you'll have access to other means to get to Fiji. Earn enough miles in the RTW or Circle fare and you can go to Fiji on an award, maybe.