Defrost the octopus by placing it in a bowl of lightly salted water in the refrigerator, until pliable or overnight. Press out the beak. Clip the eyes from the head and discard. Turn the hood inside out and discard the viscera. Wash and rinse thoroughly under cold running water.

Preheat oven to 300 degrees. Place the octopus in a deep ovenproof pan and cover, without adding water. Place in oven and cook until the octopus is bright pink-red and feels tender, turning the octopus frequently, about 1 1/2 hours. Drain the octopus in a colander and rinse under cold running water. Rub off the skin and discard. Shake the octopus dry, rub the flesh with the coarse salt and leave to dry on a towel-lined plate or baking pan in the refrigerator, covered, at least 2 hours.

Cut the chilled octopus into 2-inch pieces and tightly pack into a 1-quart jar.

In a small saucepan, combine the olive oil, vinegar, oregano, bay leaves, sugar, salt and pepper, and bring to a boil. Pour the liquid over the octopus in the jar. Add the lemon pulp, and if necessary pour in olive oil until the marinade covers the octopus. Cover, cool, and refrigerate overnight, or up to 1 week.

Remove jar from the refrigerator about 1 hour before serving.

Preheat a grill. Skewer the octopus pieces, reserving the marinade. Grill the octopus until browned along the edges and heated through, turning once and brushing with the reserved marinade. Serve with lemon wedges.