Stuff like this, water damage and insulation make me think we are putting walls together wrong. I have no idea what the solution is but this is the pits.
Interior finish work is expensive, doing it over to put in insulation is even moreso. And to add insult to injury, the low R value of walls is a data point used by siding installers, to try to talk you out of ripping the old stuff off before installing new. Each layer has an R value, dontchaknow...