Preheat the oven to 375 degrees F.
Select a wide 2 to 2 1/2-quart baking dish or casserole, large enough to hold 8 cups of fruit and 1 to 2 inches of crumble, and set aside.
Prepare the topping: in a large bowl combine the sugars and stir with a fork to break up any lumps of demerara. Blend in the flour. With a pastry blender or by rubbing the mixture roughly between your fingers, cut in the butter until the crumble begins to lump together. (The crumble may also be prepared up to this point in a food processor fitted with a steel blade: whir the sugars together to break them up, then add the flour and whir just to mix. Add the diced butter and use quick pulses to reduce the mixture to a lumpy crumble. Transfer the crumble to a bowl and proceed with the rest of the recipe by hand.) Add the coconut and the macadamias and work these by hand, kneading the mixture until evenly moist and crumbly, then set aside.
Prepare the fruit: cut the pineapple, papaya, and mango flesh into roughly 1-inch chunks and combine in large, non-reactive bowl. Peel and slice the banana, then add to bowl. Sprinkle the fruit with lime juice and toss gently to coat. In a small bowl, combine the sugar and tapioca, then toss with the fruit. Don't forget to taste! If not sweet enough for your liking, add another few tablespoons of sugar. If the sweetness is more that you care for, add another squeeze of lime.
Spoon the fruit into the baking dish. Sprinkle the crumble mixture evenly over the top. Be generous! I like to have every bit of fruit covered with a good inch or so of sweet crunchy topping. Set the dish in the preheated oven and bake for about 45 minutes, or until the topping is a rich golden brown in spots and the juices from the fruit are visibly bubbling up through the crumble. Remove from the oven and cool at least 20 minutes before serving. (The crumble may be baked up to 2 days ahead and reheated in a 350 degree F oven for 15 minutes before serving.) Serve warm or at room temperature, with vanilla ice cream or a dollop of thick yogurt, lightly sweetened with flavorful honey.