Cook jumbo pasta shells in salted boiling water until just past al dente (8-10 minutes). Drain and cool.
Sauté diced onion in olive oil and butter until translucent; add minced garlic. Cook chopped shrimp until opaque, then mix with crab, lobster, cream cheese, sour cream, half of the mozzarella, Parmesan, herbs, and seasonings.
Make the cheese sauce by melting butter, whisking in flour, then gradually adding warmed milk and heavy cream until thickened. Stir in Gruyère and remaining cheeses; season.
Preheat oven to 375°F (190°C). Spread some cheese sauce in a greased baking dish. Stuff pasta shells with seafood filling and arrange them in the dish. Pour remaining cheese sauce over shells and top with extra mozzarella.
Cover with foil; bake for 25 minutes. Uncover and bake for an additional 10-15 minutes until bubbly and golden.