Set up a large pot of boiling water. Add the red wine vinegar, garlic head halves, 1/2 cup salt, 4 of the bay leaves and 1 bunch of thyme. Bring back to a boil, then add the tripe. Simmer for 25 to 30 minutes. Remove the tripe from the water and slice into strips; set aside.
Add 2 cups of water to a small saucepan. Add the dried guajillo chiles and turn on the heat. Bring to a boil, then turn off the heat and allow to rehydrate for 10 minutes. Add the contents of the pan into a blender and puree until smooth. Set aside.
Preheat a grill pan to high heat. Add the corn and char on all sides, 5 to 7 minutes. Cut the kernels from the cobs and set aside.
Season the pork shoulder with salt. Heat a large saute pan with 2 tablespoons of the extra-virgin olive oil. Sear the pork shoulder, in batches, until brown on all sides. 5 to 7 minutes.
Coat a large Dutch oven generously with remaining 2 tablespoons extra-virgin olive oil and turn on the heat to medium high. Add the onion, minced garlic and jalapeno and saute until the onion is translucent, 5 to 7 minutes. Add the cilantro stems, lime zest and juice and 2 cups of the chicken stock. Reduce for 5 minutes.
Add the tomato paste, remaining 3 bay leaves, remaining 1 bunch thyme tied with string and the remaining chicken stock. Bring to a boil, then reduce to a simmer. Add the coriander, cumin, sliced tripe and 1/2 cup of the pureed guajillo chile mixture to the soup. Add the seared pork shoulder and squash. Simmer the soup on medium to medium-low heat, about 30 minutes. Finish the soup with half the charred corn and 2 tablespoons of the pureed guajillo chiles.
Set up a deep fryer with canola oil and heat to 350 degrees F. Fry the corn tortillas until crispy, 3 to 4 minutes. Remove to a paper towel-lined plate. Season with salt.
Crush the toasted pumpkin seeds and mix with the pumpkin oil.
Ladle the soup into bowls. Garnish with the remaining charred corn, crispy tortillas, pumpkin seeds and oil and cilantro leaves.