Combine 4 cups of the orange juice and 1 cup of the lime juice and zest in a large saucepan over high heat and reduce to 2 cups. Remove from the heat and stir in the remaining orange juice and lime juice add a few cloves of garlic and 1/4 cup of the oregano. Let cool to room temperature.
Using a paring knife, make small slits over the entire surface of the pork and rub the garlic into the slashes. Whisk together the oil and remaining 1/4 cup of the oregano in a large roasting pan, add the pork and turn to coat, cover and let marinate in the refrigerator for at least 4 hours and up to 24 hours.
Preheat the oven to 425 degrees F.
Remove the pork from the refrigerator 30 minutes before roasting. Season the pork with salt and pepper and cook for 30 minutes. Reduce the heat to 375 degrees F and continue roasting, basting with the marinade during the last 30 minutes of roasting until golden brown and an instant-read thermometer inserted into the center reaches 150 degrees F. Remove from the oven, baste with any remaining glaze, tent loosely and let rest 15 minutes before slicing.
Using a mortar and pestle, mash the garlic, serrano, cilantro and a few pinches of salt until it becomes a paste. Add the orange juice, lime juice and oil and stir to combine.
Heat butter in a large saute pan over high heat. Add the sugar and cook until melted. Add the plantains and cook until soft and heated through. Remove pan from the heat, add the rum, return to the heat and cook until the alcohol has reduced.