We just finished gutting all plaster/lath on a 1905 brick apartment and I’m trying to figure out one insulation detail:  The entry stairwell is directly against a brick wall and cannot be changed.  I have about 1.25 inches of space to work with including wall covering, so not much can be done.  The finish should be drywall and I’d like at least a small amount of insulation.

1)how to frame?  wood furring strips mechanically fastened to the brick?
2)how to insulate?  1/2 inch foil faced polyiso with very careful detailing? spray foam?

Overall insulation plan if you are curious:
climate zone 4a
-4 inches of polyiso with staggered seams above flat roof sheathing (already done)
-dense pack cellulose or fiberglass on underside of roof deck between joists (12 inches).  smart vapor barrier keeping it in.
-steel 1 5/8 inch studs offset 1 inch from the wall 1.5 – 2 inches of spray foam on all exterior walls all the way to the roof deck (except the stairs)