Position a rack in the bottom shelf of the oven and preheat to 375 degrees F. If using a muffin pan that's not nonstick, spray with nonstick cooking spray.
Whisk together the flour, baking powder, baking soda and salt in a medium bowl.
Stir together the brown sugar, rum and 3 tablespoons of the coconut oil in a small bowl. Pour about 1 tablespoon into each cup of a 6-cup nonstick jumbo muffin pan.
Place 1 pineapple ring in each muffin cup, then put 1 cherry in the center of each pineapple ring.
Finely mince the remaining 2 pineapple rings until the texture resembles crushed pineapple; transfer to a large bowl. Add the lime juice, coconut milk and granulated sugar and the remaining 4 tablespoons coconut oil. Whisk to combine. Add the flour mixture and stir with a rubber spatula until just combined.
Divide the batter among the muffin cups (about a heaping 1/4 cup in each). Use the back of a small spoon to smooth the tops. Transfer the muffin pan to a rimmed baking sheet. Bake until the center springs back when you lightly press the top a cake, about 20 minutes, rotating the pan halfway through baking.
Remove from the oven and let cool for 10 minutes. Set a wire rack inside another rimmed baking sheet and spray the rack with nonstick cooking spray. Run a small offset spatula around the edge of each cake, then carefully invert the cakes onto the prepared rack. Let cool for 20 minutes more.
Meanwhile, remove the chilled heavy coconut cream from the refrigerator. Scoop the solid coconut cream from the top of the can (about 1 cup), leaving behind the coconut water and reserving it. Whip the coconut cream with a handheld mixer on high speed in a large bowl until smooth, creamy and very soft peaks form. If the cream is too thick, whip in 1 teaspoon of the reserved coconut water at a time until you reach the desired consistency. Add the lime zest and confectioners' sugar and mix on low speed until just combined.
Top the cakes with large dollops of the whipped coconut cream. Serve immediately.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)