Peel and section the oranges over a small saucepan to catch any juice. Place orange sections in a large bowl; set aside.
Add the 1/4 cup fresh orange juice, honey, and ginger to the orange juice in saucepan. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes. Remove from heat; cool slightly. Gently stir in apple slices until coated with liquid.
Meanwhile, add pineapple, mango, kiwifruits, and carambola to orange sections in bowl. Pour apple slice mixture over fruits; stir gently to coat. Cover and refrigerate for 2 to 24 hours, stirring once. To serve, garnish with pineapple mint, if desired. Makes 10 servings.