It's edible and delicious right now. The higher internal temperature is so the meat breaks down and becomes pullable.
If you run out of time, you can go with chopped pork. In a lot of places, restaurants serve chopped pork rather than pulled pork. Just take out the meat when you need it and chop it up into small pieces for sandwiches.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan