For filling: Combine chopped pineapple, mango, papaya, brown sugar, orange juice, cinnamon stick, orange peel, lemon peel and ground cloves in heavy medium saucepan. Cook over low heat until reduced to 1 1/2 cups, stirring frequently, about 1 1/2 hours. Remove cinnamon stick. Cool.
For crust: Using electric mixer, beat butter, sugar, vanilla extract and salt in large bowl just until blended. On low speed, gradually add flour, beating just until dough begins to come together. Turn dough out onto floured work surface. Gather dough into ball; divide into 2 pieces, 1 slightly larger than the other. Flatten each piece into square. Wrap each in plastic; chill 15 minutes.
Preheat oven to 375°F Roll out larger dough piece on lightly floured work surface to 10-inch square. Transfer dough to 9-inch square metal baking pan. Press dough onto bottom and 1/2 inch up sides of pan. Pour filling into crust. Roll out remaining dough piece on floured surface to 9-inch square. Cut into 1-inch-wide strips. Place 4 strips atop filling, spacing evenly. Place 5 more strips diagonally atop first 4 strips, forming lattice. Trim lattice edges.
Bake until crust is golden brown, about 50 minutes. Cool completely. Cut into 9 squares. (Can be prepared 1 day ahead. Store in single layer in airtight container at room temperature.).