First question only, are you not removing all the exterior siding? If not, why not? If you do, you could install that exterior foam board called house wrap that has insulation and a vapor barrier and would really help you with your dellima.
Then you could snap a line at every 2x4 stud and then nail the siding back to the exterior wall and be set.
this will not work if you are not removing all the siding on the exterior because you will have a difference in suface level just like in your bath area.