Preheat charcoal or gas grill with greased grill rack for direct cooking over medium heat (350°).

Combine ½ cup mint, sugar, and water in small saucepan. Simmer over medium heat until sugar dissolves, stirring frequently. Remove mint syrup from heat; discard mint and cool completely.

Grill 3 round watermelon slices 2 to 3 minutes or until slightly charred, turning halfway through. Place strawberry halves in a large grill basket. Grill 2 to 3 minutes or until slightly charred, stirring frequently. Cool slightly.

Remove and discard rind from grilled watermelon; chop watermelon. Place watermelon and strawberries in a large blender; cover and blend until smooth. Strain through fine-mesh sieve set over bowl; discard pulp. Add 4½ cups juice mixture to small pitcher. Refrigerate any remaining juice mixture for another use. Add mint syrup and lime zest and juice to pitcher; stir to combine. Cover and refrigerate until ready to serve.

To serve, fill 6 (12-oz. each) cocktail glasses with ice. Add 6-oz. chilled juice mixture and 1½ oz. bourbon to each glass; stir to combine. Garnish with additional mint, grilled watermelon wedges, and strawberry slices, if desired.