Got it! That sounds smart. Now one last little wrinkle. That existing exterior wall that I will tear the dry wall off to insulate because I want it as one of the walls of my new space, is higher/taller that the space I am creating.
In other words, the wall is maybe 12 or 13 feet high and the ceiling of my new space will be coming off it at only 8 feet. Part of the ceiling is a mezzanine storage area build onto the wall and I will be extending that out (adding posts to the floor) and using that as the ceiling of my new space.
So, do I have to tear off and insulate all 12 feet high of that wall

, or tear off the bottom 8 feet of wallboard, put in a vapor barrier along the 8 foot level and then out and down over my new baffle insulation. I hope the latter will work because I can't open up the entire height of the wall with the mezzanine there and it is too high and probably overkill anyway.
Thanks for all the tips so far, gentlemen.