Place first 10 ingredients in a large bowl and mix thoroughly. Reserve 1⅔ cups watermelon-vegetable mixture in a bowl and set aside. Put rest of mixture in a blender and blend until smooth. (This may take a couple batches). Pour in a large bowl and add tomato juice or puree, lemon juice, lime juice, seasoned rice wine vinegar, Tabasco, Sriracha, Old Bay Seasoning and stir. Put in refrigerator to chill 30 minutes.
While soup is chilling, cut reserved watermelon-vegetable mixture to ½-inch cubes (medium dice). Place in refrigerator to chill.
Take soup from refrigerator, and season with salt and pepper to taste.
To serve, ladle soup into individual bowls. Put about ⅓ cup of watermelon-vegetable mixture in center of bowl. Sprinkle about 1 tablespoon goat cheese around mixture. Sprinkle about 1 tablespoon herb mixture over soup. Dot with smoked paprika oil and basil oil, if using. Sprinkle Aleppo pepper over top.