Preheat oven to 350°F (325°F for dark finish pans). Grease and flour 10-inch Bundt or tube pan. Combine apricots and 1/4 cup water in microwave-safe dish. Microwave at full power for 1 minute. Set aside for 10 minutes to plump; finely chop.
Whisk together flour, baking powder, allspice and salt in medium bowl. Beat butter, sugar, extract and one egg with electric mixer in large bowl until blended. Beat in remaining eggs, one at a time until blended. Beat on high speed until light and fluffy, 3 minutes, scraping down sides occasionally.
On lowest speed, alternately add flour mixture and coconut milk in 3 additions, scraping down sides of bowl as needed. Beat in 1 cup coconut and apricots on lowest speed, just until combined. Spoon into prepared pan and spread level.
Bake just until top springs back when touched in center and cake begins to pull away from pan, 55 to 65 minutes. Transfer pan to wire rack to cool for 10 minutes. Invert onto wire rack and set over waxed paper or plastic wrap.
Stir together sugar, coconut milk and lemon rind in medium bowl until blended. Brush over cake while still warm, using up all the glaze. Sprinkle top with remaining 2 tablespoons coconut.