Hmm... Assuming each type had an island in close proximity to all the others, here's how I think it would go down:
Likelihood of survival index: Low, Fair, Average, Likely, Good
ESTP - Would quickly assemble and determine the best course of action. Said action would most likely be to start a brewery with whatever vegetation they could most easily find on the island, and then start a series of competitions to determine who the leader would be (Not that anyone would follow him/her anyway). Becoming restless, many would make a swim for it (whether they make it or not would heavily depend on how much of said brewed alcohol was involved in their decision) Likelihood of survival: Fair
ESFP - Would probably start off a bit scattered with everyone running about taking in the sights (smaller groups/cliques would form at this time). Eventually hunger would cause them to gather together and create a feast of island fair. Over time they would construct a small village but would probably never get around to electing a leader. Would probably strike off in small groups to discover other islands and adventures. Likelihood of survival: Fair
ISTJ - Would come together to look at the practical solutions and whether survival would even be feasible. Would create an absolutely functional system of governance with strict rules and laws. Their town would be stripped of everything but the bare essentials, and cooly they would expect that their demise was inevitable. Because of their efficiency though, they would do better than they could ever foresee and would create one of the most efficient islands. Likelihood of survival: Average
ISFJ - Would start off with nobody wanting to take control. Groups of two or three would form and houses (as traditional as possible) would pop up over the island. A small town would eventually form and a leader selected. Everyone would be expected to follow the rules set down by said leader but no type of enforcement would be created (Unless a ESTP somehow manages to swim over, than a makeshift jail would promptly be created). Likelihood of survival: Fair
ENTP - Would start out either in a giant fight over who was in charge or with everyone trying to start their own town. Eventually the dominant alpha would take over all these towns and create one large city. Once bored, they would create a navy and go out and start taking over neighboring islands (The INTPs would be the first to be taken). Likelihood of survival: Good
ENFP - Would start out by throwing a beach party and making friends with everyone. Once the novelty wears off though, they may try to build boats to go investigate other islands. A small town might be started, but no government would be attempted.
May become the mediators/traders between the different islands. Likelihood of survival: Fair
INTJ - Would quietly observe their surroundings for a time, and then slowly come together to create a proficient system to live by. Emotion would be kept to a minimum, and everything would be done with firm logical reasoning. Would send out spies to observe other islands and steal/modify the ideas they deemed most proficient. (Would also know that the ENTPs were on to conquest before even the ENTPs knew it, and would quickly create a lethal system of defense) Likelihood of survival: Average
INFJ - Would tentatively come together, setting up a make-shift governance based on inclusion. Everyone would create their own house in small clusters with others, (I'm guessing there would be a lot of little tree-houses with swinging bridges to connect them) and privacy would be respected. Their main occupation would probably be the writing of books which the ENFPs would happily distribute to other islands for them. Likelihood of survival: Fair
ESTJ - Would probably start out with a war of words about whose system of governance was better. After an uneasy settlement is reached, some would throw themselves in to create a town and others would set out and establish themselves on another island as a leader or director. There would be absolutely no tolerance for disrupting the system once it was established, and law enforcement would be the highest compared to all other islands. Likelihood of survival: Likely
ENTJ -Would begin by having a heated debate on whose ideas to follow. Whoever best defended their stance would be respected and followed. Together they would quickly create an efficient government (based on debate) and build a practical town. Would probably become one of the most efficient islands (along with the ISTJs) with everything and everyone having their places. Likelihood of survival: Likely
ISTP - Would come together fairly easily. Some would establish themselves as directors and a town would probably be built in a matter of days. Governance would be kept to a minimum as well as small talk. Would probably be the best built town/city of all the islands and would soon have electricity and functioning vehicles, not to mention running water and an aesthetic appeal. Likelihood of survival: Likely
INTP - Would debate with one another over the best way to create a town and system of governance. Neither would ever be created. Instead, individuals would set up whatever shelter they could manage, and a committee might be formed to argue over different issues that would be raised, such as finding food and what to do about the ENTPs that seemed to be set on conquering them (Being conquered would actually be the best thing that could happen to them and might ensure their survival). Likelihood of survival: Low
ESFJ - Would all pitch in their views on how things ought to be done. Arguments about how to set up their island would inevitably break out. When a stray ESTJ showed up looking for people to direct, they would quickly become organized and fall into the roles assigned for them. An active town would soon be established and the directing ESTJ would have plenty of advice to listen to (this may or may not end with him/her fleeing from the island screaming) Likelihood of survival: Fair
ENFJ - Would probably come together very easily, listening to everyone's ideas and then creating an agreed upon system of governance. Would soon send out representatives to learn more about the other islands and might join the ENFPs in being mediators/advisers (May also help the ENFPs set up their own governance). Would find they were not welcomed by the INTJs (Remember those lethal traps? Ouch). Likelihood of survival: Likely
ISFP - Would probably set up individual living spaces tastefully decorated and integrated with nature. There would be little governance, but a booming art district would emerge (once again happily distributed by the roving ENFPs who would also be their biggest market). No big towns would be established, and from a distance their island might look uninhabited (the only indicator being the large colorful art pieces waving lazily in the breezes). Likelihood of survival: Fair
INFP - Would probably be reluctant to share their ideas, and little communication would happen for a time as everyone would escape into their own worlds. Once they were drawn out by the necessities of life, they might be able to form a make-shift government in order to reach out to their neighbors for help. Might be taken under the wings of the ENFJs and ENFPs and join them in their wanderings. Likelihood of survival: Low
Disclaimer: All this is said tongue in cheek and should not be taken seriously.
That was so in depth, it must have taken a lot of thought, haha! MAJOR kudos to you!!!