Wash rice in a colander until water runs clear. Combine rice, 1 cup water and salt in a large saucepan; bring to a boil. Reduce heat; cover. Simmer until water is absorbed and rice is tender, 15-20 minutes. Remove from heat. Let stand 10 minutes. Combine rice vinegar and sugar, stirring until sugar is dissolved. Stir into rice.
Place ⅓ cup rice into each of four 1-pint wide-mouth canning jars; layer with half of the avocados, crabmeat, cucumber and nori. Top with remaining rice and repeat layers. Cover and refrigerate until serving. Transfer into bowls; toss to combine. Serve with toppings as desired.
