Preheat oven to 350°F. Spray a 9x5 inch loaf pan with nonstick baking spray containing flour. Set aside.
In a large bowl, whisk together flour, baking powder, salt, and lime zest. Set aside.
In the bowl of a stand mixer, beat together butter and sugar until light and fluffy. Add in eggs, beating after each addition. Add vanilla bean paste, milk, and 1/4 cup coconut milk. Beat again to incorporate. Fold in crushed pineapple and flaked coconut.
Scrape batter into prepared loaf pan and bake in preheated oven for 60-70 minutes, until a tester inserted in the center of the bread comes out clean. If top begins to brown too quickly, cover lightly with foil.
Remove from oven and cool on wire rack in pan for one hour. Turn out bread onto wire rack to cool completely.
In a small bowl, mix together remaining 1/4 cup coconut milk, confectioners’ sugar and rum until no lumps remain. If needed, add more confectioners’ sugar to thicken or add more rum to thin until desired consistency is reached. Drizzle glaze over cooled cake.