Heat oven to 350°. Butter 2 (8-inch) cake pans, line with parchment, then butter the paper.
Combine mango and pineapple in a large bowl and cover with boiling water. Let sit until cooled, stirring occasionally, about 15 minutes. Drain well and set aside.
Whisk together eggs, orange zest, juice, and vanilla in a large measuring cup; set aside.
Combine pecans, coconut, and ¼ cup flour in food processor. Process until finely ground. Transfer pecan mixture to bowl of standing mixer fitted with paddle attachment. Add remaining 1¾ cups flour, sugar, salt, baking powder, baking soda, and cloves. With mixer set on medium-low speed, add butter, 1 piece at a time, until mixture is crumbly and resembles wet sand.
Slowly add egg mixture, scraping down sides of bowl as necessary. Increase speed to medium-high and beat until batter is fluffy, about 2 minutes. Decrease speed to low and add fruit 1 scoop at a time. Give batter a final stir by hand.
Divide batter between prepared pans. Gently shake and tap on counter to distribute evenly and smooth top. Bake on center rack until golden and toothpick inserted into center comes out clean, about 30 minutes.
Cool in pans for 20 minutes. Run knife around edges, carefully invert cakes onto a cutting board, remove parchment, and invert again onto cooling rack. Let cool completely.
To make buttercream:
Combine butter and salt in bowl of standing mixer fitted with whisk attachment. Beat on medium-low speed until smooth. Slowly add confectioners' sugar and beat until smooth, scraping down sides of bowl as necessary, about 2 minutes. Add rum and vanilla and mix until combined. Increase speed to medium-high and beat until light and fluffy, about 5 minutes.
Process pecans in food processor until finely ground.
Divide each cake into 2 equal rounds by cutting through the middle, making 4 cake layers. Arrange one layer on serving dish, top with ½ cup buttercream and spread to an even layer. Top with another cake layer and repeat until you have 4 iced layers. Lightly frost the sides and press ground pecans onto the sides. Garnish with candied orange peel and refrigerate until chilled. Best sliced cold. Serve cold or bring slices to room temperature before serving.