In a food processor with a metal blade, combine the chopped vegetables, shallots, garlic, horseradish, and cilantro. Puree the mixture until slightly smooth. Add the vegetable juice, vodka, Worcestershire sauce, juice from 2 lemons and the liquid crab boil. Puree until the mixture is smooth. Season with cayenne, salt, and pepper. Remove the mixture from the food processor and refrigerate for 6 hours, so the flavors can marry.
Bring a pot of salted water to a boil. Add the vegetables and blanch for 1 minute. Remove and shock the vegetables in a bowl of ice water. Remove the vegetables and pat dry.
In a mixing bowl, whisk the extra-virgin olive oil and remaining lemon juice together. Add the herbs and whisk well. Season with salt and pepper. In a mixing bowl, toss the brunoise vegetables with 1/4 cup of the vinaigrette and season with salt and pepper. Toss each of the seafood with the remaining vinaigrette. Season with salt and pepper.
To assemble, place a pile of each seafood in the bowls. Ladle the gazpacho into each bowl. Spoon the vegetable relish in the center of each bowl. Garnish with the herb salad.