Bring a large saucepan of generously salted water to a boil. Meanwhile, in a heavy 3-quart stockpot, heat the refogado and 2 tablespoons oil over medium-low heat, then stir in the rice. Season with salt. Cook, stirring, until the rice is toasted, 3 to 4 minutes.
Stir in 1⁄2 cup of the stock. Cover, reduce the heat to low, and simmer for 5 minutes. Stir in the remaining 2 1⁄2 cups stock. Bring to a simmer, cover, and cook just until a soft bite remains, about 15 minutes.
While the rice simmers, drop the lobster tail and claws into the boiling water. Cook the tail for 4 minutes and the claws for 6 minutes. Transfer to a cutting board. When cool enough to handle, shell and cut the meat into chunks.
Divide the vinho verde, garlic, and cilantro sprigs between two medium saucepans. Bring to a boil. Add the mussels to one pan and the clams to the other. Cover and cook just until the shellfish open. Immediately transfer to a plate. Strain the cooking liquids through a fine-mesh sieve and reserve.
With a sharp knife, score both sides of each scallop in a crosshatch pattern. Season with salt and pepper. Heat a large skillet over high heat until it is very hot. Lightly coat with oil and heat until lightly smoking. Add the scallops in a single layer. Cook, pressing flat with a spatula, until brown, about 1 minute per side. Transfer to a plate. Repeat with the shrimp, cooking just until orange, about 10 seconds per side.
Gently stir 1⁄4 cup of the reserved shellfish liquid into the rice. Season with salt and pepper. Fold in the lobster, mussels, clams, shrimp, and scallops and heat for 2 minutes. Arrange the sea urchin tongues on top. Drizzle with oil and sprinkle with the lime zest, chopped cilantro, and fleur de sel.