Preparing the glaze: Combine the pineapple juice, orange juice and vinegar in a saucepan over high heat. Bring mixture to a boil. Reduce heat to medium-low and simmer about 25 minutes, until mixture is reduced to 3/4 cup. Pour 1/2 cup of the juice mixture into a small bowl. Set aside to cool, about 30 minutes. Once cool, add lime juice and mint, stir to blend, set aside. Brush the remaining 1/4 cup of glaze on fruit while grilling.

Preparing the fruit: Use a melon ball cutter to scoop out 4 cups total from the honeydew and cantaloupe, or cut the melons into 2x1-inch pieces. Cut the pineapple into 2x1-inch pieces. Alternate each skewer with honeydew, pineapple, and cantaloupe leaving about 3/4-inch of the skewer exposed at the blunt end. Wrap with foil to prevent burning.

Grilling: Preheat the grill to 375F (or a medium-hot fire). Leave fruit skewers on a hot, lightly oiled grill until golden brown and slightly charred. Brush with reserved glaze on each side during last 30 seconds of cooking, 3 to 4 minutes per side. Remove foil and arrange kebobs on individual serving plates, drizzle with minted glaze and serve.