Prepare Ginger-Plum Sauce; set aside.
Combine next 11 ingredients in a medium bowl. Place 1 mame nori sheet on a dry work surface with a short end toward you. Using moistened fingers, place about 2 teaspoons of the rice along the short edge farthest from you. Place a dry lettuce leaf on the bottom third of wrapper. Spread 1/3 cup crabmeat mixture on top of lettuce. Top with 4 slices each of avocado and mango. Place another dry lettuce leaf atop avocado and mango. Starting with short edge closest to you, fold wrapper over filling. Roll toward top edge of wrapper (toward the rice), pressing firmly. (The rice will keep the roll closed.) Lay roll seam-side down, and repeat with remaining ingredients.
Cut each roll into 4 pieces, and place on a serving platter. Serve with Ginger-Plum Sauce.