Preheat oven to 400°.
Lightly spoon flour into dry measuring cups; level with a knife.
Combine 1/4 cup flour, peaches, honey, juice, and 1/4 teaspoon salt in a large bowl; toss gently. Let stand 15 minutes. Fold in blackberries. Spoon mixture into a 13 x 9-inch baking dish coated with cooking spray.
Combine 2 cups flour, 1/2 teaspoon salt, granulated sugar, rind, and baking powder in a medium bowl, stirring with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add buttermilk, and stir just until moist.
Drop dough onto peach mixture to form 12 mounds. Sprinkle mounds with turbinado sugar. Bake at 400° for 40 minutes or until bubbly and golden.