I would like to insulate my exterior walls. Here is the issue, the wall is made up of the following: Brick exterior, 1" air gap, studs (no sheathing) and 1/2" GWB. If I have insulation blown in, masonry absorbs moisture and the insulation will get wet since the insulation will fill the entire gap, thus a mold problem.

I also looked into 'shaving-cream' style foam, but if they add too much it will blow out the gwb, plus it creates a solid mass. If water gets behind the brick, where does it go since the closed cell insulation will not absorb the moisture.

Any suggestions other than ripping all the interior gwb down, insulating and reinstalling the gwb?