Clean the tripe (quick but worth it). Rinse tripe well. Soak in cold water with the juice of 1 lime (or 2 tablespoons vinegar) for 15 to 20 minutes, then rinse again and drain.
Start the tenderizing simmer. Add tripe to a large pot with 10 cups water, the halved onion, 3 garlic cloves, bay leaves, and 1 tablespoon kosher salt. Bring to a boil, then reduce to a gentle simmer. Cover partially and cook for 2 1/2 to 3 1/2 hours, stirring occasionally. Skim foam or excess fat as needed. Tripe is ready when it is tender and pleasant to chew, not bouncy or rubbery.
Instant Pot option: Pressure cook tripe with the same aromatics for 45 minutes, then natural release for 15 minutes. Check tenderness. If it is still firm, pressure cook for 10 to 15 minutes more and release again.
Soften the dried chiles. While the tripe cooks, toast guajillo, ancho, and optional árbol chiles in a dry skillet over medium heat for 30 to 60 seconds, just until fragrant. Add to a bowl and cover with very hot water. Soak for 15 minutes.
Blend the sweet and spicy chile sauce. Add softened chiles to a blender with 1 cup of chile soaking water, remaining 3 garlic cloves, cumin, Mexican oregano, smoked paprika (if using), vinegar, and 1 tablespoon honey (or the drained crushed pineapple). Blend until very smooth.
Blender safety note: If anything is warm, do not seal the lid tight. Vent the lid (or remove the center cap and cover with a towel), and start on low to prevent pressure buildup.
If you want a silky broth, strain through a fine mesh strainer. If you used pineapple, straining is optional but it will give you a smoother finish.
Bloom the sauce. Using a slotted spoon, transfer the cooked tripe to a bowl. Carefully pour the broth into a second pot or heat-safe container (you are just making room to toast the sauce). Set both aside.
Return the empty main pot to the stove. Heat 1 tablespoon oil over medium heat. Carefully pour in the chile sauce and cook for 3 to 5 minutes, stirring. This step makes the flavor taste deeper and less raw.
Build the menudo broth. Pour the reserved broth back into the pot with the bloomed chile sauce, stirring as you go. Return the tripe to the pot. Simmer uncovered for 30 minutes so everything meets in the middle.
Add hominy. Stir in drained, rinsed hominy. Continue simmering for 25 to 35 minutes, until the tripe is truly tender and the broth tastes unified. Add a splash of water if it gets too thick.
Dial in seasoning. Stir in the remaining 1/2 tablespoon kosher salt to start, then adjust to taste. Add more honey, 1 teaspoon at a time, if you want a rounder sweet heat. Finish with a big squeeze of lime and a pinch more oregano right before serving.
About the “lighter” vibe: This is lighter in the sense that it is broth-forward and we skim fat as it cooks. It is still a bold, salty, classic-tasting soup. Season to your comfort.
Serve like you mean it. Ladle into bowls and top with diced onion, cilantro, radish, and lots of lime. Tortilla on the side for scooping is not optional in my kitchen.