Heat the oil in a large Dutch oven. Add the bacon and cook over medium until crisp. Add the onion and cook until beginning to brown, about 5 minutes. Whisk in the flour and cook until lightly browned, about 2 minutes. Whisk in the fish stock and bring to a simmer. Add the potatoes, turnips, parsnips, celery root, and thyme; simmer over until tender, about 20 minutes.

Add the milk and cook, stirring occasionally, until the soup is thickened, about 10 minutes. Stir in the snapper, lemon juice, Worcestershire, and a dash of hot sauce and cook until the fish is just white throughout, about 5 minutes. Stir in the parsley and season with salt and pepper. Transfer the chowder to bowls and garnish with dill. Serve, passing more hot sauce at the table.