Set a Dutch oven over medium heat and add the chopped bacon and olive oil. Cook for 6 to 8 minutes until the bacon is browned and crisp and the fat has rendered out, leaving the bacon and fat in the pot.
Add the diced onion, celery, carrots, and green bell pepper to the pot and cook over medium heat for 7 to 9 minutes until the onion turns translucent. Stir in the minced garlic and cook for 1 more minute until fragrant, without browning.
Push the vegetables to one side and add the tomato paste to the open spot in the pot. Cook the paste for about 1 minute, stirring it into the vegetables as it darkens slightly.
Add the cubed potatoes, undrained diced tomatoes, bottled clam juice, reserved juice from the canned clams, and water or chicken broth. Stir in the bay leaves, dried thyme, dried oregano, red pepper flakes, and Worcestershire sauce, then scrape the bottom of the pot to lift any browned bits.
Bring the pot up to a gentle boil, then lower the heat to keep a steady simmer. Cover partially and simmer for 20 to 25 minutes until the potatoes are fork-tender but still holding their shape, then season with salt and black pepper.
Stir in the drained chopped clams and cook for just 3 to 5 minutes more, keeping the heat low and avoiding a hard boil so the clams stay tender.
Remove and discard the bay leaves, stir in the chopped fresh parsley, and taste one last time for seasoning. Ladle into bowls and serve hot with oyster crackers or crusty bread.