For the dressing: Combine all the gomatare dressing ingredients; mix well and set aside.
For the eel sauce: Place all the sauce ingredients in a saucepan, and heat to simmering. Cook for 10 minutes; strain through a fine chinois, and place in a container or bottle.
For Solstice roll: Place the crab, kewpie mayonnaise, scallion and sesame oil in a bowl, and mix to combine. Refrigerate. Place 2 tablespoons of crab mixture on each premade sheet; add the cut tempura shrimp across the crabmeat from end to end, and roll. Then add the sliced avocado over the top of the rolled sushi and place a piece of plastic film over the roll. Using the mat, squeeze lightly to make the roll firm. (Slice the roll while the plastic wrap is still covering it.) Drizzle the gomatare dressing over the top. Add the eel sauce, and sprinkle with toasted sesame seeds. Slice into 6 to 8 pieces.
For sushi rice: Place 2 cups of raw sushi rice in a rice steamer. Cover with 2 cups water, 1/2 cup mirin and 2 tablespoons of the rice wine vinegar; cook for about 20 minutes. Turn rice cooker off and let rice cool in cooker, cover with lid for about 30 minutes. Remove and place cooked rice in a large mixing bowl. Using a wooden spoon, stir rice and add 2 more tablespoons of rice wine vinegar, stir until well incorporated and let cool at room temperature.