I never trip the fat cap... though I do score it in a diamond pattern... and mine goes right on the rack, no need to wrap unless trying to hurry through a stall, then after it's rested, pull meat apart in a foil pan and let the mat soak up any juices in the pan.
Another mistake some people make is pulling out all the fat and discarding it. At 203F IT (the goal) there's going to be a few pieces inside that will never render, but the rest of the fat is like gold.. squish it between your fingers as your pulling the pork apart and mix it in. This helps retain moisture and flavor and aids if you reheat it .