Preheat the oven to 300 degrees. In a large bowl, toss the pork with the salt, cumin, oregano, chili powder, and paprika until completely coated.
In a 6 quart dutch oven or large heavy bottom pot, heat 2 Tablespoons of the avocado oil (or lard) over medium-high heat. Sear the pork in batches of about 3 pieces on all sides until brown, adding more oil as needed.
Remove from pot. Do not drain any excess grease. Reduce the heat to medium.
Add the onions and sauté for 5 minutes.
Add the garlic and sauté for 1-2 minutes. Deglaze the pot with the orange and lime juice, scraping any brown bits off the bottom of the pot.
Pour in the Coke and bring the mixture to a boil.
Add the seared pork and any juices from the plate back into the pot so they are submerged in the braising liquid.
Add the orange rinds and bay leaves on top.
Cover and bake for 3 hours.
Remove the pork from the pot and shred it with two forks. It should be extremely tender.
Transfer the shredded pork back into the pot with all of its juices.
Optional: Spread shredded pork onto a large sheet pan in an even layer and broil until crispy. Assemble tacos.