When I do BRITU, I use the minion method even though the directions say otherwise. If I were in your shoes, I would put the meat on after about an hour even if the temp is a little high.
I think you are right though in that you might have air leakage. When you shut everything down after a cook, how long does it take for the fire to go out? Or when you're cooking, do you barely have to have your vents open to hold a temp of about 275? That or a long time for the fire to go out, would suggest a leak and the door is the first and easiest place to start. Try bending the door a little (carefully). You shouldn't need tape.