Halve and juice fruit; reserve juice for another use. Put peels in a large pot and cover with cold water. Bring to a boil and cook 3 minutes. Drain. Return peels to pot, cover with cold water, bring to a boil, cook 3 minutes, and drain. Repeat once more. Spread peels on baking sheets and let sit until cool enough to handle, 20 minutes.
Using a soup spoon, scrape out the membranes and discard. Cut peels into strips and set aside.
In a large, heavy pot over high heat, bring 8 cups water and 6 cups sugar to a boil. Add peels, reduce heat to maintain a steady, gentle simmer, and cook, stirring occasionally, until peels are tender, sweet, and translucent, 3 hours. (Don't let sugar brown or caramelize.) Drain peels and spread on wire racks set over baking sheets. Let sit until dry, at least 8 hours.
Toss a handful of peels with remaining 2 cups sugar. Shake off excess sugar and put in an airtight container. Repeat with remaining peels.
Note: Nutritional analysis is per 1/4 cup.