Not an island but for a uniquely Greek experience with very few tourists you could try the Mani peninsula – best summed up as the Deep South of Greece with all the usual deep south features like family feuds that go on for generations, rugged independence from national government, large calibre firearms, hospitality to strangers. You seem like a libertarian, you’ll probably love it.
We’ve been a couple of times, last time the room in Areopoli [named after Ares the god of war] had a Boys anti tank rifle on the balcony. Bit corroded but the action was greased up ready to go, just in case.
You can also swim past the cave that is the traditional gate to Hades.
More about it in Mani by Patrick Leigh Fermor, who live there – his other stuff is worth a read too.