1. Puree the Italian plum tomatoes in a food processor or blender. Strain them through a fine sieve set over a large bowl; discard the tomato seeds.
2. In a large enameled cast-iron casserole, heat the extra-virgin olive oil until shimmering. Add the smashed garlic and cook over moderately high heat until fragrant, about 30 seconds. Add the pureed tomatoes, the clam juice, thyme, basil and sugar. Season with salt and pepper and bring to a boil. Cook over moderately low heat until it is reduced by one-third, about 45 minutes. Add the squid and cook over low heat until very tender, about 45 minutes longer.
3. In a large pot of boiling salted water, cook the linguine until al dente. Drain the pasta well and return it to the pot.
4. Add the mussels and cockles to the tomato sauce, cover and cook the sauce over moderately high heat until most of the shells have opened, 3 to 5 minutes. Add the shrimp and cook until they are pink and firm, about 2 minutes longer. Discard any unopened mussels and cockles. Pour the tomato-seafood sauce over the cooked pasta and toss over high heat for 2 minutes. Transfer the pasta and sauce to a large warmed bowl, sprinkle with crushed red pepper and serve.
Make Ahead: The tomato-seafood sauce can be prepared through Step 2 and refrigerated overnight. Bring to a simmer before proceeding.
Wine Recommendation: A light, bright white with sharp acidity will point up the shellfish and hint of red pepper in this dish. Try a Gavi such as the 1999 Coppo La Rocca or the superb 1999 La Scolca White Label.