Combine sea salt, black pepper, thyme, garlic powder, rosemary, and paprika in a bowl. Place hens on a baking sheet and evenly brush with 5 tablespoons butter. Rub hens with spice mixture.
Bake hens in preheated oven until no longer pink at the bone and the juices run clear, about 1 1/2 hours, basting every 1/2 hour with white wine. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 180 degrees F (82 degrees C).
Mix cherries, red wine, orange juice, and brown sugar in a saucepan; bring to a boil for 2 to 3 minutes. Reduce heat to medium-low, stir in 2 tablespoons butter, and cook until sugar is dissolved and butter is melted, about 10 minutes. Sprinkle flour into the sauce; whisk until thickened, 2 to 3 minutes. Drizzle cherry sauce over cooked hens.