For the coconut pecan crumb: Use a food processor to grind the oats, pulsing the machine until the oats resemble coarse cornmeal.
Whisk the ground oats, flour, sugar, cinnamon, ginger, nutmeg, and salt together in a medium bowl. Add the melted butter and mix with your fingers or a fork until small clumps form. Add the pecans and coconut and mix lightly. Chill the crumb for 15 minutes before topping the pie.
For the pie: Lightly flour a smooth work surface and a rolling pin.
Take a chilled disk of dough out of the fridge. Give it a couple of firm squeezes just to say hello, then unwrap it and set it on the floured work surface.
Set the pin crosswise on the dough and press down firmly, making a nice deep channel across the full width of the disk. Turn the disk 180 degrees and repeat, making a second indentation, forming a plus sign.
Use your rolling pin to press down each of the wedges, turning the dough 45 degrees each time. This will give you the beginnings of a thick circle.
Now, rolling from the center outward and rotating the dough a quarter turn to maintain a circular shape, roll the dough out to a 13-inch circle with an even thickness of ¼ inch.
Set your 9-inch (23-cm) pie pan alongside the circle of dough. Brush off any loose flour, carefully fold the dough circle in half, transfer it to the pan, and unfold.
At this point, the dough will be lying across rather than fitted into the pan. Now, without stretching the dough, set the dough down into the pan so that it is flush up against the sides and bottom. The best way to do this is to gingerly lift the dough and gently shift it around so that it settles into the pan bit by bit. Use a very light touch to help cozy it in.
To flute the edge, fold the overhang under to form a 1-inch wall that rests on the lip of the pan with the seam slightly below the pan’s top edge. Go around the edge of the pan and use a very light touch to firm up the wall to an even thickness from the bottom to the top and all the way around. Flute the edge of the crust at about 1-inch intervals, pressing from the inside with the knuckle of your index finger while supporting on the outside with the thumb and index finger of your opposite hand. Don’t pinch the dough, you want the flute to look like a thick rope.
Transfer the crust to the refrigerator to chill while you make your filling. Alternatively, at this point the crust can be covered tightly in plastic wrap and refrigerated for up to 3 days or double-wrapped and frozen for up to 2 months (defrost overnight in the refrigerator before filling and baking or prebaking, or at room temperature for 30 minutes).
Preheat the oven to 375°F with a rack in the center. Line a rimmed baking sheet with parchment paper.
Whisk the brown sugar, cornstarch, nutmeg, cinnamon, and salt together in a small bowl.
In a large bowl, combine the pineapple, bananas, dried apricots, lemon juice, and rum, tossing lightly to mix. Sprinkle in the sugar mixture and toss well, coating the fruit and thoroughly moistening the cornstarch and sugar.
Retrieve the prepared pie shell from the refrigerator and set the pan on the parchment-lined baking sheet. Scoop the filling into the pie shell and top with the crumb. Transfer the baking sheet to the oven and bake the pie 25 minutes, then rotate the baking sheet, lower the oven temperature to 350°F, and bake another 25 to 30 minutes, or until the juices are bubbling (mine baked an additional 15 minutes beyond that). Tent the top with foil if the crumb starts to over-brown.
Set the baking sheet on a wire rack and let the pie cool and set, uncovered, at room temperature overnight (or up to 3 days) (mine cooled about 6 hours, which was plenty of time for it to set while retaining its flaky crust), before slicing and serving with vanilla ice cream.