In a blender, purée 1 cup of melon, lime juice, 3 tablespoons of sugar, and a pinch of kosher salt until very smoot. Add a splash of water at a time, if necessary, so that the mixture liquefies.
Strain melon juice with a fine mesh sieve into a bowl, pressing out the solids. Add more lime and sugar to taste. (Note: purée will taste slightly less sweet once frozen).
Meanwhile, toss the remaining 3 cups of melon with the remaining tablespoon of sugar, salt and Maras chile flakes.
Divide the chile spiced melon chunks evenly between popsicles molds and top with the melon juice. Leave about 1/2 - 3/4-inch empty for expansion. Add popsicle mold lid, insert sticks and freeze until fully frozen and solid, 4-8 hours depending on your freezer but preferably, overnight.