Place 1 teaspoon pomegranate seeds in 8 of the wells in a 16-cube ice tray; drop red currants in remaining 8 wells. Fill wells with water. Freeze into ice cubes, 8 hours to overnight.
Combine chopped cranberries, water, and sugar in a saucepan over low heat. Simmer, stirring frequently, until cranberries have completely softened, about 15 minutes.
Strain cranberries through a fine mesh sieve, gently pressing the pulp to extract the liquid. Let syrup cool before covering, then refrigerate 8 hours to overnight.
Use a clean needle to thread popcorn and dried cranberries onto one long food-grade thread. Cut into 8 equal strings.
Add 1 pomegranate ice cube and 1 red currant ice cube to each serving glass. Pour 2 tablespoons syrup into each and top with 3/4 cup tonic water. Garnish with a lime wedge and a string of popcorn and cranberries.
