Fresh Coconut Layer Cake

INGREDIENTS

• 3 large egg whites, at room temperature 30 minutes
• 1/8 teaspoon salt
• 1 1/2 tablespoons light corn syrup
• 2 (1 1/2-pound) coconuts
• 1 3/4 cups sugar, divided
• 2 1/4 cups sugar
• 3 1/3 cups sifted cake flour (not self-rising; sift before measuring)
• 3/4 cup water
• 1 tablespoon baking powder
• 1 1/2 cups whole milk
• 1/4 cup sugar
• 1 teaspoon salt
• 1 teaspoon pure vanilla extract
• 1 1/2 teaspoons pure vanilla extract
• 1/2 teaspoon cream of tartar
• 2 1/2 sticks unsalted butter, softened
• 1/8 teaspoon pure almond extract
• 7 large egg whites, at room temperature 30 minutes