Cook pasta according to package directions, omitting salt and fat. Drain and set aside.
Preheat oven to 375°.
Coat 2 (13 x 9-inch) baking dishes with cooking spray; set aside.
Place cottage cheese and ricotta cheese in a food processor; process until smooth. Combine cottage cheese mixture, Asiago, and next 6 ingredients (Asiago through spinach).
Spoon or pipe 1 tablespoon cheese mixture into each shell. Arrange half of stuffed shells, seam sides up, in one prepared dish. Pour 3 cups Smoky Marinara over stuffed shells. Sprinkle with 1/2 cup mozzarella. Repeat procedure with remaining stuffed shells, Smoky Marinara, and mozzarella in remaining prepared dish.
Cover with foil. Bake at 375° for 30 minutes or until thoroughly heated.
To freeze unbaked casserole: Prepare through Step 5. Cover with plastic wrap, pressing to remove as much air as possible. Wrap with heavy-duty foil. Store in freezer for up to 2 months.
To prepare frozen unbaked casserole: Preheat oven to 375º. Remove foil; reserve foil. Remove plastic wrap; discard wrap. Cover frozen casserole with reserved foil; bake at 375º for 1 hour and 10 minutes or until the shells are thoroughly heated.