Place bacon in a large, heavy saucepan and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels. Pour bacon drippings into bowl and reserve.
Melt 1 tablespoon butter in the same saucepan over medium-high heat. Cook and stir onions in hot butter until soft, 5 to 8 minutes. Add potatoes, 1/2 the bottle of clam juice, celery, carrots, mushrooms, 1 1/2 teaspoons pepper, and 1 teaspoon salt. Bring to a simmer, reduce heat to medium-low, cover the saucepan, and cook until vegetables are just tender, about 15 minutes.
Melt 1/2 cup butter in a large pot over medium heat. Whisk flour into melted butter until smooth. Whisk milk, half-and-half, and cream into flour mixture until smooth and slightly thickened, about 10 minutes. Stir vegetable mixture, bay leaves, thyme, and dill into cream mixture. Bring to a simmer, reduce heat to medium-low, and simmer until vegetables are tender and chowder is hot, 15 minutes.
Stir minced clams, spinach leaves, and reserved bacon drippings into chowder. Cook until clams are heated through, 3 to 5 minutes. Season with salt and pepper to taste.
