First, that's an awesome set up, and you'll love it!
I would shy away from mesquite as it is a very powerful wood and imparts a LOT of flavor. Maybe mix a couple chunks of apple and one chunk of mesquite if you are set on using it.
I'd recommend at least 1.5 hours per pound, and then give yourself an extra hour or two in case the shoulder has a long stall.
There are two schools of thought..
Wrap it with foil when you get 160 degree internal temp, or let it go without foil and get more bark, which is what I prefer
Also, I hate smoking on my weber at 225-250, I've actually been running my temps from 275-300 for pork butts/shoulders as I prefer the texture and bark I get with a little higher heat, and I don't have the patience for a 12-15 hour smoke any more.
Looking at the recipe, the first thing I see is an injection, which I've never done, so I can't speak to that. Others will post with opinions better than mine when it comes to that aspect.
I'd cook it until you hit 200-205 for an internal meat temp, wrap in foil, and place in a cooler with a towel covering it for an hour, at minimum. This will allow time for the juices to soak back into the meat. Just as a side note, you can store cooked butts/shoulder in a cooler this way for hours, and they'll still be too hot to pull with bare hands most of the time.
Good luck, keep us updated, and post pictures.