In a medium saucepan, combine the ketchup, water, vinegar, brown sugar, mustard, onion powder, chili powder, pepper, salt, cloves, lemon juice, and Worcestershire sauce. Bring the mixture to a boil over medium high heat, then reduce the heat to medium low and simmer for 1 hour, stirring frequently, so the flavors meld nicely.
Place the pork in the slow cooker, and add the carrots, onion and garlic, then pour in 1 ½ cups of the sauce and stir to combine. Cook on low heat for 6 to 8 hours.
Take two forks and use them to pull apart the meat right in the cooking liquid. This should be very, very easy. Toss the meat so it gets well coated with the sauce and juices. Remove it with a slotted spoon.
Pile the meat on the buns and serve with additional sauce and the salsa of your choice.