Preheat oven to 350 degrees F.
In a large bowl, combine the cookie crumbs, coconut and butter until evenly incorporated. Transfer to a 9-inch pie plate and press down and up the sides until completely covered. Bake for about 10 to 15 minutes or until golden brown. Remove from the oven and let cool completely.
Whisk together the sugar and cornstarch in a medium saucepan. Whisk in the crushed pineapple and stir in the strawberry slices. Cook over medium high heat until it comes to a boil, continuing to whisk nonstop. Cook until thickened, about 1 minute. Remove from heat and let cool down completely.
In a bowl of a stand mixer fitted with the whisk attachment, beat the cream cheese until smooth. Slowly beat in 1 cup of the cream of coconut until well combined. Add the eggs, one at a time, mixing well after each addition. Stir in the rum.
Spread the cooled pineapple and strawberry mixture onto the bottom of the cooled pie crust. Pour the cream cheese mixture all over the top. Bake for about 35 to 40 minutes or until the custard is set. Remove from the oven and let cool for about 1 hour on a wire rack. Cover with plastic wrap and let chill for about 4 hours or overnight.
Beat the heavy whipping cream on high until slightly thickened, lower the speed and slowly whisk in the remaining 1/2 cup cream of coconut. Continue to beat on high until soft peaks form. Top the chilled pie with the coconut cream and sprinkle with toasted coconut. Cut and serve or place in fridge until ready to serve.