Bring the water and rice to a simmer in a large saucepan over high heat. Reduce the heat to low, cover, and cook until the rice is tender and the water is fully absorbed, 45 to 50 minutes. Remove the pot from the heat, lay a clean folded dish towel underneath the lid to trap steam, and let it rest for 10 minutes.

Combine the vinegar, mirin, and sugar in a small saucepan and bring to a boil, then remove from the heat. Transfer a portion of this vinegar mixture to a small bowl and whisk in the soy sauce, ginger, orange zest and juice, and lime zest and juice to create the dressing. Move the cooked rice to a large bowl, drizzle with the remaining vinegar mixture, and let it cool for 20 minutes, tossing gently with a wooden paddle or spoon occasionally.

Spread the tofu over a paper towel-lined baking sheet and let it drain while the rice cooks. After 20 minutes, gently press the tofu dry with fresh paper towels and season with salt and pepper.

Heat the oven to 200°F and place a paper towel-lined plate inside. Set a wire rack over a rimmed baking sheet. Whisk the cornstarch and cornmeal together in a shallow dish, then coat several pieces of tofu at a time, pressing firmly to help the coating adhere before moving them to the wire rack.

Heat half the oil in a 12-inch nonstick skillet over medium-high heat until shimmering. Fry half of the tofu until crisp and lightly golden on all sides, 10 to 12 minutes, then transfer to the plate in the oven to stay warm. Repeat with the remaining oil and tofu.

Portion the seasoned rice into individual bowls and garnish with the nori. Top with the warm tofu, radishes, avocado, and cucumber. Sprinkle with scallions and drizzle with the reserved dressing, serving immediately while the tofu is still crackling.