Place the clams in a large bowl and cover with cold water. Add 1 teaspoon of salt and let the clams sit for 20 to 30 minutes so they can release any sand. Lift the clams out of the water and into a clean bowl, and rinse briefly under cold water. Do not pour the sandy water over them.
Rinse the mussels under cold water, scrubbing off any debris. Remove the beards by pulling firmly toward the hinge. Discard any mussels or clams that are cracked or that stay open when tapped.
Bring a large pot of salted water to a boil. Add the linguine and cook until just shy of al dente according to package directions. Before draining, scoop out 1 to 1½ cups of the starchy pasta water and set aside. Drain the pasta.
While the pasta cooks, pat the shrimp dry with paper towels and season lightly with salt and pepper.
In a wide sauté pan or shallow Dutch oven, heat the olive oil over medium heat. Add the sliced garlic and minced shallot and cook for 1 to 2 minutes, stirring often, until softened and fragrant but not browned.
Add the Calabrian chili paste or crushed red pepper, if using, and cook for 20 to 30 seconds to bloom the flavors in the oil.
Pour in the white wine and let it simmer, uncovered, for 3 to 4 minutes, until reduced by about half. This helps create a thicker base for the sauce.
Add the mussels and clams to the reduced wine mixture. Cover the pan and cook over medium-high heat for 4 to 6 minutes, gently shaking the pan occasionally, until most of the shells have opened. Discard any that stay closed.
Add the shrimp to the pan, nestling them into the liquid. Cover again and cook for 2 to 3 minutes, just until the shrimp are pink and opaque.
Add the lemon zest and about ½ cup of the reserved pasta water to the pan and gently stir.
Add the drained linguine to the pan with the seafood. Turn the heat to low and toss gently for 1 to 3 minutes, adding more pasta water a little at a time until the sauce becomes silky, glossy, and clings to the pasta instead of pooling at the bottom of the pan. Add 2 to 3 Tablespoons of butter and toss until melted and fully incorporated.
Turn off the heat. Add the lemon juice and chopped parsley, and toss again. Taste and adjust with more salt and black pepper as needed.
Divide the pasta and seafood into bowls and serve immediately.