Preheat oven to 375 degrees F (190 degrees C). Grease a 9-inch baking pan.
Melt 1/2 cup butter in a skillet over medium heat. Add celery and onion; cook and stir until browned, 6 to 8 minutes. Mix in thyme, seasoned salt, parsley, black pepper, nutmeg, oregano, and marjoram.
Transfer herb mixture to a large bowl. Add cubed bread and 2 cups chicken broth; toss until well combined. Spread stuffing evenly over the prepared pan.
Bake in the preheated oven until golden brown, about 30 minutes.
Place Cornish hens on a flat work surface. Sprinkle salt inside the cavities.
Heat olive oil in a large skillet over medium-high heat. Add hens; season exteriors lightly with salt and pepper. Cook, turning to press all sides into the oil, until browned, 10 to 12 minutes. Remove hens from heat, reserving the oil.
Spoon stuffing into the hen cavities; place hens in a slow cooker. Pour the reserved olive oil, wine, and 1/4 cup chicken broth into the slow cooker. Sprinkle sage, savory, and rosemary over the hens. Slice butter into 4 separate tablespoons and place on hens.
Cook hens on Low until tender and juicy and an instant-read thermometer inserted into the thickest part of the thigh, near the bone, reads 165 degrees F (74 degrees C), about 8 hours and 30 minutes.