Juice oranges and lemons, discarding seeds and reserving rinds. Set juice aside.
Put reserved orange and lemon rinds into a large bowl, sprinkle with citric acid and cream of tartar, and toss to combine. Pour 2 cups boiling water over rinds and set aside to let steep for 15 minutes. Strain fruit-infused liquid, discarding rinds, and set aside.
Put sugar and 2 cups water into a medium pot and cook over medium heat until the sugar is dissolved. Place sugar syrup aside to let cool.
To make concentrate, combine reserved fruit juices, fruit-infused liquid, and sugar syrup in a 2-quart glass jar with a tight-fitting lid (Wright uses a clean pickle jar). Stir well with a wooden spoon. Cover and refrigerate for at least 2 days and up to 2 weeks before using, to let the flavors come together. When ready to use, mix 1 part fruit punch concentrate with 3 parts water. Serve over crushed ice, if you like. Refrigerate leftover concentrate for up to 2 weeks.