Lucky guests of the lauded, exclusive and pricey (funny how those three things so often go together) Little Palm Island Resort & Spa  are welcomed into the elegant Shore Station where bags are whisked away, cars are parked (you won’t need them where you’re going) and hands are filled with a glass of champagne or a refreshing Gumby Slumber—the resort’s signature rum punch—made from coconut rum, spiced rum, pineapple, orange and cranberry juice topped with a “shot" of shredded coconut that’s been marinated in 151 proof rum.

And you haven’t even reached the island resort yet.

To do that, you board one of three petite wooden-hulled yachts that the resort operates for its guests. After a sunny and smooth 15 minute ride on The Truman (which has leather seats in a shade of...