Heat a large skillet over medium heat and add 1 tablespoon of the vegetable oil. Add the turkey to the pan and brown until it is no longer pink and the meat crumbles, 8 minutes. Remove the turkey from the pan and set it aside in a bowl or plate. Add the other tablespoon of oil to the pan, followed by the carrot, onion and 2 tablespoons of the pineapple juice, and cook until the onion becomes translucent, 8 to 10 minutes. Add the tomato paste and cook for 2 minutes. Next, add the chicken stock, ketchup, mustard, Worcestershire sauce, tomato sauce and the remaining pineapple juice. Bring to a boil, reduce to a simmer and cook uncovered until thickened and reduced by one third, 15 to 20 minutes. Add the cooked turkey to the sauce and stir to combine. Cook for 6 to 8 minutes, to warm through. Season with salt and pepper.
Scoop the sloppy lo mixture evenly onto the buns and top with the pickles. Serve with 14 napkins, preferably near a bathtub.