To split hens, use a sharp knife to cut along both sides of the breastplate, through the breastbone and along both sides of the backbone.
Melt 1 tablespoon of the butter in a medium saucepan over medium-high heat. Add onion and celery; cook, stirring often, until onion is tender, about 5 minutes. Add garlic and cook, stirring constantly, for 1 minute. Stir in rice; cook, stirring constantly, for 1 minute. Stir in chicken broth and bring to a boil. Reduce heat to low; cover and simmer until rice is tender and liquid is absorbed, about 1 hour and 5 minutes. Stir in grapes, chopped thyme, ½ teaspoon of the salt and ¼ teaspoon of the pepper. Transfer to a bowl; let cool for 15 minutes.
Preheat oven to 425°F. Place a wire rack in a foil-lined large rimmed baking sheet; coat rack with cooking spray. Stuff warm rice mixture into cavities of hens; tie ends of legs together with kitchen twine and tuck wing tips under. Place hens breast-side up on rack. Rub with remaining 2 tablespoons butter and sprinkle with remaining 1½ teaspoons salt and ¾ teaspoon pepper. Bake until golden brown and a thermometer inserted into thigh registers 160°F, about 35 minutes.
Meanwhile, combine vinegar, honey and thyme sprig in a small saucepan; bring to a boil over medium-high heat. Boil, stirring occasionally, until mixture is syrupy and reduced to about ¼ cup, 7 to 8 minutes. Discard thyme sprig.
After hens have baked for 35 minutes, brush with vinegar mixture. Continue baking until hens are deeply browned and a thermometer inserted into thigh registers 165°F, about 10 minutes. (Shield hens with foil if needed to prevent excessive browning.) Remove from oven and let stand for 10 minutes. Split hens in half length