To make the pickled carrots, stir together the sushi vinegar, sugar, salt, ginger and soy sauce. Fold in the carrots and let sit overnight. Drain before serving.
Place the cucumbers on a parchment-lined baking sheet and sprinkle with salt. Let them sit for 30 minutes, then pat dry with paper towels. Whisk together the sugar and rice wine vinegar in a bowl until the sugar dissolves. Add the cucumbers.
Rinse the rice in cold water and drain three times. Place the rice and water in a saucepan, bring to a simmer, cover, and cook until the grains are tender, 15-20 minutes.
In a small bowl, combine the rice wine vinegar, sugar and salt until the salt is dissolved. Season the cooked rice with vinegar mixture.
Whisk together all of the vinaigrette ingredients and let stand for 1 hour before using. Shake well and season to taste with salt and pepper just before dressing the dish.
To assemble the bowls, divide the sushi rice between bowls. Top with tuna, mizuna, radishes, picked cucumbers and carrots. Drizzle with octo vinaigrette and sprinkle with furikake and green onions.