Preheat the oven to 325 degrees F (165 degrees C).
Pulse graham crackers, 1/2 cup coconut, and powdered sugar for crust together in a food processor until finely ground. Add butter; blend until well combined. Press mixture firmly into the bottom and up the sides of a 9-inch metal pie pan. Crust will be generous.
Bake in the preheated oven until lightly browned, 12 to 15 minutes.
Beat egg yolks in a bowl with an electric mixer on medium speed until thick and light in color, about 4 minutes. Beat in sweetened condensed milk, 2 minutes more. Stir in mango puree and lime juice. Pour mixture into crust.
Bake until just set in center when gently shaken, about 30 minutes. Cool pie completely and chill at least 2 hours.
To make topping, beat together egg whites, white sugar, and salt in a bowl set over a pan of simmering water. When sugar dissolves and mixture is hot to the touch, 3 to 4 minutes, remove from heat. Beat with an electric mixer until stiff peaks form, about 10 minutes. Transfer mixture to a piping bag with a large open tip or a zip-top plastic bag with 1/2 inch of a corner snipped off. Pipe onto chilled pie.
Set an oven rack 6 inches from the heat source and preheat the oven's broiler to low heat.
Broil pie in the preheated oven just until top is toasted, 2 to 3 minutes, watching closely to avoid burning. Sprinkle with coconut.