I'm looking for some advices on how to go about insulating an old wall exterior wall. The house date 1930 and behind the plaster we only have a 1inch air gap made of 1 inch rough strapping and then black paper (then its wood planks and bricks). The nort side wall I can reframe a 2x4 wall and insulate normally with fiberglass but the east side I have a window and a door so adding 5 inch to the wall is not an option. Spray foam is not an option (doing this myself) and I heard bad stories about DYI using 2 component spray foam so I was wondering if using 1 inch rigid foam then adding strapping over it for air space and drywall could be an ok option.
Edit: This is in Montreal so cold climate ;)