Cut the eggs in half horizontally. Remove the yolks to a food processor. Add the mayonnaise, cocktail sauce, tomato paste, horseradish, paprika, hot sauce and lemon juice and process until smooth. Transfer to a pastry bag and set aside.
Spread a tablespoon of seafood seasoning on a small plate. Slice a bit off the bottom of each egg white half so it stands up and forms a little cup. Dip the top of each egg white half in the seafood seasoning, then pipe in the filling. Garnish with the olive slices, celery matchsticks and celery leaves.