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Cut the watermelon pulp from the rind, leaving a thin layer of pink.
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Peel the green outer skin from the rind and discard. Cut enough rind into 1x1 1/2-inch pieces to measure 4 cups.
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In a large pot, combine the water and 2 tablespoons of kosher salt. Bring to a boil. Add the rinds and boil until they are tender, about 5 minutes. Strain and transfer to a metal bowl.
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While the rinds boil, combine the remaining 2 teaspoons of kosher salt, sugar, apple cider vinegar, cloves, peppercorns, cinnamon sticks, pickling spice, allspice and ginger in a heavy saucepan. Bring to a boil, and stir until the sugar dissolves.
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Pour the brine over the drained rinds. Place a plate on top of them to make sure they stay submerged.
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Refrigerate for at least an hour or up to 2 weeks.
