Grease the sides and bottom of a 9×13 inch baking dish and dust with some shredded coconut.
In a bowl of a stand mixer fitted with a whisk attachment, sprinkle the gelatin over ½ cup of the water. Let stand for a few minutes to soften.
In a heavy bottom saucepan, combine the sugar, corn syrup, remaining ½ cup water, and salt over low heat. Stir until sugar is dissolved. Increase heat to medium and let bring to a boil. Continue to cook mixture, without stirring, until a candy thermometer reads 240°F. Immediately poor over the gelatin in the stand mixer, stirring until gelatin is dissolved.
Beat the mixture on high speed until white, thick, and tripled in volume, about 6 minutes. Meanwhile, beat the egg whites until they just hold stiff peaks. Add the egg whites, and vanilla and coconut extracts to the gelatin mixture and mix until combined.
Pour the mixture into the prepared pan and sprinkle generously with shredded coconut. Let sit uncovered for at least three hours, and up to one day.
Use a knife to cut around the edges and cut the marshmallows into squares, greasing the knife if necessary. Toss the marshmallows in more shredded coconut to cover the now exposed sticky edges.
Store the marshmallows in an airtight container at room temperature for up to one week.