Here's a place where we can deposit our Utopia. The Kingdom of Jerusalem controlled Aquaba from early in the 12th century through to about 1187. We can imagine our Europeans departing somewhere in the 1150s, perhaps deciding to escape the civil war that afflicted the kingdom of that time.
The Portuguese began to explore our little corner of the Indian ocean in the 1530s. That gives us around 350 years for initial development of our little community, and a further 200 from that rediscovery until our period of interest; a bit longer before the expansion of exploration makes discovery unavoidable later in the 18th century.
Records from the middle ages are scant enough to allow the disappearance of hundreds or even thousands of people to go unnoticed. We can put the last 200 years down to the work of the Society of New Jerusalem. The early explorers who returned to report small desert islands in the area came back wealthy -- and carefully watched -- men.