Combine 3/4 cup lime juice, 1/3 cup sugar and 3/4 cup water in a bowl; stir until dissolved. Pour into an ice cube tray and freeze until firm, 1 to 2 hours. Meanwhile, line a baking sheet with plastic wrap; spread out the melon chunks, cover and freeze until solid, 1 to 2 hours. (The lime ice cubes and melon can be frozen up to 2 days ahead.)
Make the white layer: Combine the lime ice cubes, tequila, orange-flavored liqueur and 2 cups plain ice cubes in a blender and process until slushy. Transfer to a small pitcher or bowl; cover with plastic wrap and freeze, about 2 hours. Rinse out the blender.
When ready to serve, make the red layer: Combine the frozen strawberries, elderflower liqueur, 1/4 cup lime juice, 1/3 cup sugar and 2 cups plain ice cubes in the blender; process until slushy. Transfer to another small pitcher or bowl and set aside. Rinse out the blender.
Make the green layer: Blend the frozen melon, mint, the remaining 1/4 cup lime juice and 1/3 cup sugar, 1 1/2 cups plain ice cubes and 1/2 cup water until slushy.
Rub the rims of 6 glasses with a lime wedge, then dip in coarse salt. Fill each glass one-third of the way with the green slush; spoon a layer of the white slush on top, then finish with the red slush. Serve with lime wedges. (The individual slushes or the assembled drinks will keep up to 3 days in the freezer. Thaw 20 to 40 minutes before assembling or serving.)