Thread shrimp onto skewers and place in a shallow dish. Pour 1/2 cup soy sauce, sake, and 2 tablespoons oil over the shrimp and season them with salt and pepper. Set aside and let them marinate while you make the barbecue sauce.
Heat 3 tablespoons oil in a large saute pan over medium-high heat. Add shallots and garlic and cook for 1 minute. Stir in tomatoes and season with salt and pepper. Add 2 tablespoons soy sauce, hoisin sauce, vinegar, chili paste, sugar, and chili powder. Cook until the mixture has thickened, about 10 to 15 minutes. Use an immersion blender to break the tomatoes up into a chunky sauce.
Heat a grill or a grill pan and cook the shrimp about 3 minutes per side. To serve, spread some barbecue sauce onto a large platter and place the grilled shrimp skewers on top of that. Garnish with avocado, scallions, and lime wedges. Serve extra barbecue sauce on the side.