I don't know... I think the best way to close a island would be to progressively increasing the rogue spawns (x2 every week or something like that) and give some kind of reward to the 'survivors' every day (or week): Gold, Prestige, Honour, items, scrolls or any other thing.
In the end all the island would be destroyed by the monsters, but the nobles who resist more weeks before left the island would have some important advantages.
It would be a way to compensate the lost of their island, and make a kind of 'survival competition'.
Another idea nobody has said... Use the weather: The chosen island weather go immediately to 'severe drought' or 'endless winter'... Medieval Mad Max!
The 'civilization' will die not destroyed by monsters (at least not only) but destroyed by starvation!
Of course, surviving will receive rewards too.
