Then let it rest for an hour or so and pull/enjoy.
Pork butts never finish for me in the time others say it will take. I used to try waking up early to put them on and I was always stressing because they take forever.
I now just put them on at about 10PM, wrap them at 8AM and pull them off the smoker to rest around 10-11AM. Then let them rest in a cooler until we eat, usually in the afternoon or evening. If you are worried about the temp going too low during resting then you can also just keep them warm in the oven at 170 for as long as you need.
Putting them on the night before completely eliminates the stress over whether they will be done at a specific time for a meal.