In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the granulated sugar, the brown sugar, baking soda, and salt. Beat until combined, scraping bowl occasionally. Beat in eggs, vanilla paste, and coconut extract until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Stir in the 1 cup coconut, the candied pineapple, and the citrus peels.
Divide dough into thirds. Shape each third of the dough into a 12-inch-long roll. Wrap rolls in plastic wrap or waxed paper. Chill for at least 4 hours or up to 24 hours or until firm enough to slice.
Preheat oven to 350 degrees F. Cut rolls into 1/2-inch-thick slices. Place slices 1 inch apart on an ungreased cookie sheet. Bake for 9 to 10 minutes or just until centers are set. Transfer cookies to a wire rack; cool.
For glaze, in a medium bowl stir together the powdered sugar and enough of the lemon juice to make an icing of drizzling consistency. Drizzle tops of cookies with the glaze; sprinkle with additional toasted coconut. Let stand until glaze is set.