Florida Ambrosia Salad

Preheat the oven to 400°F.
Pierce the softest eye of the coconut with a metal skewer or small screwdriver and drain any liquid into a small bowl to sample—you should have about 1/2 cup liquid. (If the liquid tastes sweet, the coconut is fresh; if it tastes oily, the coconut is rancid and should be discarded.)
Bake the coconut for 15 minutes then transfer to a folded towel on a work surface. Using the back of a knife or a cleaver, crack the shell open. Break the shell into large pieces and use a strong knife to carefully remove the flesh from the shell. Using a vegetable peeler, remove the brown skin then shave the coconut into thin strips—you should have about 4 cups shaved coconut. Reserve 2 cups for the ambrosia salad; wrap and freeze the remainder for another use. DO AHEAD: Coconut shavings can stored, in an airtight container, in the refrigerator up to 1 week or frozen up to 3 months.
Using a serrated knife, cut the peel off the grapefruits and oranges. Cut the fruit crosswise into 1/2-inch-thick rounds then cut the rounds into bite-size pieces. Transfer to a large bowl; add the pineapple, kumquats, pomegranate seeds, 2 cups coconut shavings, 1/2 cup coconut juice, and the apple juice, and toss gently to combine. Serve at room temperature or chilled. DO AHEAD: Florida Ambrosia Salad can be prepared ahead and stored, covered, in the refrigerator up to 8 hours.