Pat the cod, shrimp, and scallops dry with paper towels and keep them chilled. Drain the chopped clams over a bowl, keeping both the meat and the juice. Dice the onion and celery, mince the garlic, and peel and cube the potatoes into even 1/2-inch pieces.
Set a Dutch oven over medium heat and add the chopped bacon. Cook, stirring now and then, for 6 to 8 minutes until crisp and the fat has rendered. Lift the bacon out with a slotted spoon and set it on a plate, leaving the rendered fat in the pot.
Add the butter to the bacon fat and let it melt over medium heat. Stir in the diced onion and celery with a pinch of salt and cook for 5 to 6 minutes until softened and translucent. Add the minced garlic and cook for about 1 minute, just until fragrant.
Sprinkle the flour evenly over the vegetables. Stir constantly for 1 to 2 minutes to cook off the raw flour taste and coat everything in a light paste.
Slowly pour in the seafood stock a little at a time, whisking after each addition to keep the roux smooth and lump-free. Stir in the reserved clam juice, then add the cubed potatoes, bay leaf, thyme, Old Bay, and smoked paprika. Bring to a gentle simmer and cook uncovered for about 15 minutes, until the potatoes are fork-tender.
Lower the heat to medium-low. Pour in the heavy cream and whole milk, stirring to combine, and warm gently for 2 to 3 minutes. Do not let it come to a hard boil, or the dairy can separate.
Add the cod pieces and scallops first and simmer very gently for 3 to 4 minutes. Add the shrimp and the reserved clam meat and cook for another 2 to 3 minutes, just until the shrimp turn pink and opaque and the fish flakes. Remove and discard the bay leaf.
Taste the broth and season with salt and freshly ground black pepper. Stir in half of the cooked bacon and half of the chopped parsley. Ladle into bowls and top with the remaining bacon, more parsley, oyster crackers, and a lemon wedge on the side.