For cake: Preheat oven to 350°F. Butter two 9-inch-diameter cake pans with 1 1/2-inch-high sides. Line bottoms with parchment. Butter parchment; dust pans with flour. Sift flour, baking powder, ground ginger, baking soda, salt and ground cinnamon into medium bowl. Using electric mixer, cream unsalted butter and sugar in large bowl until fluffy. Beat in eggs 1 at a time. Add unsulfured molasses, grated orange peel and vanilla extract and beat 1 minute at high speed until well blended. Mix in dry ingredients alternately with buttermilk, beginning and ending with dry ingredients. Fold in shredded coconut and crystallized ginger.
Divide batter between prepared pans. Bake until cakes begin to pull away from sides of pans, about 30 minutes. Cool in pans on rack 5 minutes. Invert cakes onto racks. Remove parchment and cool completely.
For icing: Using electric mixer, beat cream cheese and butter until smooth. Mix in orange peel and vanilla. Beat in sugar. Mix in ginger.
Place 1 cake layer on platter, flat side down. Spread with some of icing. Sprinkle with 3/4 cup coconut. Top with second layer, flat side up. Spread remaining icing over top and sides of cake. Arrange remaining coconut around top edge of cake. (Can be prepared 1 day ahead. Chill until icing is set; wrap lightly with plastic and refrigerate. Bring to room temperature.) Place fruit around base of cake.