Sorry to not be able to make you happy, but you are talking about going to the place that is the most expensive to get to and from in South America so you have no real cheap way out of it if you must include Fiji. I have found that when I have done trips to South America (from Australia) a round the world ticket is the cheapest way out of it normally and the fare you would require is not particularly cheap either. If you got a round the world ticket it would require you to leave Europe from Madrid, Barcelona or London (most likely Madrid depending on where you go first). You might be able to get out of it cheaper if you skipped Los Angeles by going to South America the fly from Santiago (or Buenos Aires) to Sydney. Buenos Aires would be better because Qantas has a direct flight where as Santiago would require you to go via Auckland. You could then go from Sydney to Nadi on Air Pacific (this would require you to get the mileage based one world rtw fare as the continent based one doesn't allow use of Air Pacific.
Doing your trip on a rtw ticket would also mean you didn't have the extra expenses of the internal flights in South America (as long as you put your flights in a good order which might mean stuff like going to Lima first and then doing the rest etc. The bus trip from Santiago to Buenos Aires or vice versa is really spectacular but it is better to do it from Santiago to Buenos Aires than the other way because at least you will get to see a lot where as the other way it was done a lot of the time during the dark so you missed a lot of stuff.
If you want some spectacular trekking you could go to Patagonia region and do something like the W Trek at Torres Del Paine NP and go glacier trekking at El Calafate. The W Trek is known to be one of the best treks in the world and is quite spectacular especially once you finally get to the towers which is why most people do the trek. Doing that you also don't need to worry about altitude sickness either. You could also trek in El Chalten which is also meant to be very spectacular but that one I did not get time to do. Around that area you can also do glacier trekking and see some great nature and scenery. It does have huts along the way that you can pay to stay in but you do really need to book those in advance especially if you are going in the peak times of year like November - February sort of time. If you are travelling outside those times it is probably too cold for it to be nice doing that trek as I know even in December it got quite cold and that is meant to be when it is hottest.
[ Edit: Edited on 17-Nov-2009, at 17:19 by aharrold45 ]