Any Fijian Iguana that you are able to obtain will be very expensive, very time consuming- you must fulfill the requirement of showing how your ownership will benefit the survival of the species before the CITES I paperwork, US paperwork and permits, possibly state paperwork and permits (private ownership rarely satisfies the requirement) and you really must ensure that the animal is legal (which would be discovered when you are doing the paperwork) or else you can get yourself into a lot of trouble.
I do not see a time in the future that an "average joe" in the US will be able to have one. It is kind of like a Komodo Dragon, but it is on the Red List, not just the Vulnerable List; it comes from a limited range, it is already classified as CITES I, and opening them up for procurement would lead to a mad rush to obtain them. I would love to have one myself in the future, but know that it probably will never be possible.
Breeding efforts have already been very successful. The San Diego Zoo has so many they do not know what to do with them all! The problem is that they are not allowed to do anything with them other than keep them. The San Diego Zoo has an agreement with the Fijian Government that prohibits them from doing anything but keep them (I believe that they are allowed to return the progeny to Fiji).
Cheers,
Michael