I would recheck regarding the adopted code allowing an AAV. I know that the code used here in Florida allows them, and IIRC, a plumbing "code help" book that I read several times that addressed both the Uniform and International codes didn't mention that one or the other code didn't allow them.
Personally, I am not the biggest fan of AAV's, but they do have their place. If it were me, I would probably cut the boards out in one stud bay and conventional vent that way. Use some batt insulation to reinsulate that cavity, and be done with it.
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