Combine 113 grams (1/2 cup) water, the gelatin, lemon, and lime juices in a 2-quart saucepan. Set aside.
Combine the remaining 170 grams (3/4 cup) water and 227 grams (1 cup) of the sugar in another 2-quart saucepan, over medium heat. Stir until the sugar dissolves. Bring to a boil, cover, and cook for 3 minutes. Remove the lid and cook until the mixture reaches 300ºF on a digital instant-read thermometer.
Once the sugar comes to temperature, remove from the heat, and add to the gelatin mixture. The mixture will clump; just reduce the heat to low and stir constantly in order to dissolve gelatin completely. Add the lemon and lime zest and stir to combine. Pour mixture into an 8-by-8-inch nonstick pan and cool to room temperature, 1 ½ to 2 hours. Do not refrigerate.
Using a pizza wheel, cut the cooled jellies into cubes, and toss to coat in the remaining sugar. Serve immediately or store in an airtight container for up to 4 days. Stored jellies may need to be recoated in sugar before serving.