In my experience the best way to store and reheat any BBQ, ESPECIALLY pulled port is to Vacuum seal it when its pulled then the next day place the vac bag (still sealed) into a pot of boiling water for a few minutes, or into a crock pot filled with warm water on the low setting (then it will take a couple hours to come to heat).
Another thing I have done 2 or 4 times if that isn't an option is to store the meat tightly like you mentioned, then the next day I put it into one of the crock pot liner bags, you can also store it in the line bag over night (you can buy these at most grocery stores) and tie up the top, then put that into either crock pot on low, or into the oven on the lowest setting. To keep the best flavor I think it needs to be sealed up the entire time, not just for the moisture but it may also absorb other flavors since the moisture level is so high. The first time I smoked a butt for a work party I stored it in the fridge loosely (though I thought it was plenty tight), then reheated in a crock pot, and though it wasn't dry because I added sauce and apple juice it had taken on a sort of strange refrigerator flavor, and clearly tasted like leftovers to me, even though perhaps others dindt notice or at least say anything.
I worked in the culinary field for many years and this is a common practice for reheating things, (vac seal and boil) there are even several BBQ joints in the US who seal up your BBQ leftovers for you with the instruction to boil it the next day. I now do that method 100% of the time and get excellent results, if it is sealed up the whole time, it will taste like it just came off of the pit. Just keep in mind that aluminum foil isn't a great seal because it doesn't seal around the edges and clear plastic wrap is actually not a great seal either because it is so thin unless you use several layers.
Also if you have saved some of the runoff juice from the cook, you can add it back in to get the moisture up if needed, and as others mentioned, you can just use something like apple juice or BBQ sauce to moisten it up if needed as well.