Make the Nonalcoholic Spirit: Combine all ingredients in a small saucepan and bring to a boil over medium heat. Cover and remove from heat immediately, and let sit 5 minutes. Strain solids through a fine mesh strainer or coffee filter, let come to room temperature, bottle, and refrigerate.
Make the Pineapple Syrup: Combine the sugar and water in a saucepan over medium heat. Stir until the sugar has completely dissolved. Add the pineapple chunks to the saucepan. Bring the mixture to a boil, then reduce the heat to low and let it simmer for about 10 minutes.
Remove the saucepan from the heat and let the mixture steep as it cools down to room temperature. This will allow the pineapple flavor to infuse into the syrup. Once cooled, strain the syrup through a fine-mesh sieve into a clean jar or bottle, pressing the pineapple chunks to extract as much liquid as possible. Discard the pineapple chunks. Store your pineapple simple syrup in the refrigerator. It should stay fresh for about a month.
Make the drink: Combine all ingredients but the lime wheel in a shaker filled with ice. Shake and strain into a tall, chilled glass. Fill with crushed ice. Garnish with lime wheel.