Line the bottom of a 9-inch springform pan with parchment. Mix the graham cracker crumbs, toasted coconut and melted butter, press firmly into the bottom of the pan and chill while you make the filling.
Drain 1/3 cup of juice from the can of crushed pineapple and set both aside. Use canned pineapple only, since fresh pineapple prevents gelatin from setting.
Blend the cottage cheese in a food processor or blender for 2 to 3 minutes, scraping down the sides, until completely silky. Add the cream cheese, cream of coconut, powdered sugar, lime juice, vanilla and rum extract and blend until smooth.
Sprinkle the gelatin over the reserved pineapple juice, let it bloom for 5 minutes, then microwave for 10 to 15 seconds until fully liquid. Whisk in 1/2 cup of the filling, pour it back into the blender with the motor running and blend for 15 seconds.
Pour the filling over the crust, smooth the top and refrigerate for 2 hours until set.
For the topping, stir the remaining crushed pineapple and its juice with the sugar and cornstarch in a saucepan. Cook over medium heat, stirring, for 3 to 4 minutes until thick and glossy, then let it cool completely.
Spread the pineapple topping over the set cheesecake and refrigerate for at least 4 hours or overnight. Release the springform ring and sprinkle with toasted coconut flakes before serving.