MALC...Welcome.
The above folks really do have you covered and you will see there are variations of the same and some these guys are a whole lot qualified than I.
Shoot everyone has thrown a bit into the fire. I know everyone will say here comes Mallard with the the Mesquite thing. One thing you will find out is that Mesquite is a heck-of-a-lot stronger than you think with the Bradley, if have smoked before and have used chunk type Mesquite in different type smokers, it will be different in that it will be lighter, less intense taste. Personally I would use 2-3 hours of that wood.
Another thing pull that butt out of the fridge and let it sit out for around 1.5hrs, this will help in the cooking time.
Also I would invest in a remote thermometer, man that takes the guess work out. The cheapest ones I have found are at "Sports Academy", around $16.00.
When it comes to hunk-O-meats like a butt, do the 225 thing. A butt takes long enough at 225 let alone 200. Good man...FTC the thing...this will help immensely and before you close the foil up put a couple splashes of apple juice in with the meat.
Let us know how things turn out...