Rinse the sushi rice under cold water until the water runs clear. In a medium saucepan, combine the rinsed rice and water. Bring to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes or until the water is absorbed. Remove from heat and let it sit, covered, for 10 minutes.
In a small bowl, mix together the rice vinegar, sugar, and salt until dissolved. Fluff the cooked rice with a fork and gently fold in the vinegar mixture. Allow the rice to cool to room temperature.
In another bowl, combine the cooked shrimp, mayonnaise, sriracha, and lime juice. Mix well to coat the shrimp evenly.
To assemble the sushi stacks, use a round mold or a small cup. Start by layering a spoonful of sushi rice at the bottom, followed by a layer of the spicy shrimp mixture, then add a few slices of avocado and cucumber. Repeat the layers until you reach the top of the mold.
Carefully remove the mold to reveal the stacked sushi. Garnish with chopped green onions and sesame seeds, if desired.
Serve immediately with nori strips on the side for wrapping, if using.