I have a full set of stairs that walk up into an unfinished attic space. The full sized access door to these stairs is in a hallway as if its a closet. Unfortunately, the max distance I have under each stair before I hit the attic-side of an interior wall (solid blue line in picture below) is only 6 inches. What is the best way to insulate this under the stairs so heat isn't lost from the interior closet pictured? I've drawn a diagram below:
One idea I have is to add rigid foam on the inside of the closet as FreeMan has recommended. But what can I add to the big void under the first 3 stairs and what about the small area behind the higher stairs?
Here is a close up shot of under the bottom 3 stairs. The prior owner put light insulation in place with the face on the inside of the attic and barely any insulation to fill the giant void:
I'm wondering if I put faced insulation against the drywall of the closet. If so, how do I secure it? There are no lumber beams to staple to. Then in front of that I loosely stack a few batts of unfaced insulation to fill up the big void?
If you are curious about the sides of the stairwell going up to the attic: they are insulated with fiberglass insulation in the wall beams and then a 2-3" rigid foam insulation in front. So when I walk up the stairs the sides are shiny silver like I'm walking into a spaceship.