Make the crust: Preheat the oven to 350˚ F. Line an 8-inch square baking dish with foil, leaving a 2-inch overhang on two sides; lightly brush with melted butter. Toss the cookie crumbs, sugar and melted butter in a small bowl until well combined. Firmly press the mixture evenly into the bottom of the pan to make a thin layer. Bake until firm and lightly browned, about 10 minutes. Let cool at least 20 minutes. Reduce the oven temperature to 325˚ F.
Make the filling: Combine the cream cheese, cream of coconut, sugar and salt in a large bowl and beat with a mixer on medium-high speed, scraping down the bowl a few times, until smooth and fluffy, 3 to 5 minutes. Reduce the mixer speed to medium; beat in the eggs, sour cream and coconut extract until combined. Spread the filling over the crust.
Bake until the edges are set but the center is still a little jiggly, 35 to 45 minutes. Transfer to a rack and let cool to room temperature, about 3 hours.
Meanwhile, make the topping: Combine the dried and crushed pineapple, cream of coconut, lemon juice and water in a small saucepan over medium-high heat. Bring to a simmer, stirring occasionally, then reduce the heat to medium low and cook, stirring occasionally, until the dried pineapple is tender and the liquid has reduced to just a few spoonfuls of syrup, about 20 minutes. Let the topping cool, stirring occasionally, 30 to 45 minutes.
Spoon the topping over the cheesecake layer and gently spread to cover. Cover with plastic wrap and refrigerate overnight.
Remove the bars from the pan, peel off the foil and cut into pieces.