Combine crayfish, breadcrumbs, half of chopped onion, green onion, celery, 1 clove minced garlic, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/8 teaspoon red pepper in a large mixing bowl; stir until well blended. Add eggs and 1/4 cup plus 2 tablespoons water; mix well.
Shape mixture into 1 1/2-inch balls. Place on a waxed paper-lined baking sheet; cover and chill 1 hour.
Melt butter in a large Dutch oven over low heat. Add flour; stir until blended. Cook, stirring constantly, until roux is the color of a copper penny. Add remaining onion and garlic; cook until tender.
Add tomato paste, sugar, and remaining water, salt, and pepper; cook over medium-low heat, stirring until thickened. Remove from heat; set aside.
Brown crayfish balls in hot oil in a large skillet over medium heat. Drain on paper towels.
Add crayfish balls to roux in Dutch oven; bring to a boil. Reduce heat; cover and simmer 1 1/2 hours. Serve over hot cooked rice in warm soup bowls.