Preheat the oven to 425°F and spray a 9×13 baking dish with nonstick spray.
In a small pot, combine rice vinegar, granulated sugar, and salt; heat and stir just until the sugar dissolves, then remove from heat.
Cook the rinsed sushi rice according to package instructions using the appropriate amount of water; once cooked, stir in 1 tablespoon furikake and 1 tablespoon toasted sesame seeds.
Press the seasoned rice evenly into the bottom of the prepared baking dish and set aside.
In a mixing bowl, combine the softened cream cheese, chopped crab meat, chopped cooked shrimp, and 1/4 cup mayonnaise until smooth and well blended.
Lay the nori sheets in a single layer over the rice to cover it.
Spread the seafood and cream cheese mixture evenly over the nori layer using a rubber spatula.
Scatter the blanched asparagus pieces evenly over the seafood layer.
Drizzle sriracha mayo and unagi sushi sauce over the top in a diagonal pattern.
Bake in the preheated oven for 15–20 minutes, until the top is hot and caramelized but not burned.
Let the casserole rest for a few minutes, then top with diced avocado, diced cucumber, scallions, and an extra sprinkle of furikake; serve warm.