For a long time, I have cooked my pork on a rack over a pan from the get-go. I don't see the point on letting any meat juices go down the grease bucket.
I do use a rub, but only one one side, as I leave the skin on, cooking it skin up. I start off at a low temp for an hour or so, before increasing it to 240°-250°. Then at 160° internal, I wrap the meat, and put it directly on the grate, which lets me take the pan inside to deglaze and start preparing the sauce. More juices usually come out of the wrapping, which also gets added to the sauce. I rest the meat for 30-60 minutes, then pull and sauce.
I almost always cook at least a day before I intend to serve. I find the whole thing improves from a night in the fridge.
Yesterday I was visiting friends who had recently received some pulled pork, and they commented how although the pork was pulled, it was still in nice big strips and chunks. Much supermarket pulled pork here (which is all they had tried before) seems to be cooked until it is almost separate fibres - I think this is because they mechanically pull the meat. I find that tastes like mush, and far prefer to have a bit of bite to my pulled pork. This is especially important, as I know it is going to be reheated.