David, I realise it is going to be quite a challenge to find somewhere that has had little attention by fishermen. A few of the places you mention are interesting - Iran, Libya and North Korea. I had already thought about Easter Island, and will be researching it further. So far most of the places that seem interesting are islands. A couple of others so far include Kruglen Island near the antarctic circle, and Socotra, in the dangerous waters between Somalia and Yemen. Just researching is fascinating enough. There are a few books available about fishing the Falklands, which is a bit of a turn off, but does not necessarily write it off the list. The Papua New Guinnea area has been covered a bit in the last few years by Col Roberts, (whom I will be interviewing for my blog in the next couple of weeks), and some of it's jungle rivers and deep reefs are well known as fishing hotspots.
Peter, I have been to New Zealand (South Island only so far), and certainly intend returning one day. A spectacular place, just not quite unique enough for my project. I am also planning a trip to Chile and Argentina with my wife as she has family there, which will be a feast of fly fishing and photography also!
Denis K, I plan on spending at least a month on the trip, so will be sure to allow plenty of time for transfers etc, but thanks - that is a great point!