I’ve been reading for days on how to go about insulating a room I demoed down to the studs.  House is 100 plus years old and  has  aluminum siding over original wood siding and no WRB.  I can insulate the ceiling without issue because I have a walk up attic above.  I furred out my stud bays with lath to match the existing molding depth.  My stud cavity depth is now measured just a tad over 4 inches.   I don’t want to fur out the walls any farther.  I am in Buffalo, NY which from my research is climate zone 6.  I know I need an air barrier for drying out moisture but how much?  With only 4 inches of cavity should I just use 2 inches of foam board and have back two inches air space.  Do I use EPS or XPS?  I’m just looking for my best option.  R value doesn’t need to be perfect I just want to add something.  I also thought about 1.5 inch foam board and ROCKWOOL sliced in half the long way 1.75 inches.  That would leave me 3/4 of air space against the back of the sheathing.  Stupid idea ?  Thoughts and recommendations on what I should do ?