Or perhaps this show is based off of "Floating Island," by Elizabeth Hayden. Maybe the island is simply a ship as described in the book. The Floating Island - Wikipedia, the free encyclopedia

And someone has built a floating island, Man (Re)Builds Mexican Island Paradise on 250,000 Recycled Floating Bottles | ecoble - ecological design, green innovation and environmental sustainability

One of the questions about the island, (first season) How was Dharma getting all the electricity? apparently, if you build a self sufficient island, you can power it also.

So, they can physically move the island with the em back up and no one would find the island again.