Bribes and Secrecy
This is an answer based on The Most Dangerous Game, by Richard Connell. In the book, the protagonist is stranded on what appears to be an abandoned island, but meets the owner of the island, Zaroff, who challenges him to become the most dangerous game. If the protagonist can stay alive for three days, Zaroff would let him go free. Zaroff then proceeds to try to hunt him down for the rest of the book.
Zaroff, in the novel, is a retired army veteran looking for fun in hunting down humans. In the book, he has already made countless victims of the previously shipwrecked people.
How was Zaroff able to maintain his hunts in relative secrecy from the rest of the world, despite them being against the laws of almost any country? He lives on an abandoned island, and most importantly, none of the hunted had ever survived.
Based on this approach, perhaps the protagonists of your book can keep their island’s sovereignty by adopting a secretive approach. On the surface, they can obtain the rights to the island and become a separate country, but maintaining the non-intrusive laws.
But in reality, they can hold their conflicting laws in the shadows. Just as in The Most Dangerous Game, they can silence any dissenters, or people who find out about their dark side.
Obviously, this act of silencing can be done in more ways than in the book; bribes, blackmail, imprisonment, and burying. The bribes, blackmail, and imprisonment would make the book more interesting, as it leaves weak points for resistance to occur. Burying would be somewhat more problematic, as it would be difficult to 'cover up' (pardon the pun).
If anything happens, however, and news starts to leak, using their finances, the group could also bribe medias and small governments to keep up the veil. Considering that, as you have said, the island itself does not hold much value in capturing, there would be more benefits to be had for any corrupt officials to receive bribes instead.
TL;DR, by maintaining secrecy (forcefully, if need be), and suppressing any leaks through their considerable finances, the group could be successful in implementing shadow policies on their island. The relative seclusion and suppression of leaks would preemptively prevent any possible attacks on the island, rather than trying to stop one.