If time is limited, cut the brine time short, and give the time to the smoke/rest. A well-brined undercooked or under-rested butt is not what you want. Remember, it is perfectly fine to smoke a butt without brining. There's lots of fat in there to keep it moist. If you are starting your smoke at 6 am, you might be eating pretty late, or might not have much time for a rest. A couple hours or more wrapped in foil, a towel, and into a cooler to rest does wonders. You can rest for 5-6 hours no problem.