Insulating Stairwell

[NoCreativity]

I built a new home a couple of years ago. I was working long days at the time so I didn't have much time to monitor construction and my wife handled most interactions with the builder. After exploring the attic I've noticed why the room below the stairs is so cold all the time.... the builder didn't insulate the outside of the stair well !! At ALL ! I'ts just sheet rock and studs... there are a few other places I've found that they skimped on insulation, otherwise it's pretty well stocked w/ blown in fiberglass. We found out later that the contractor had also had some trouble with the insulation guy on some other projects as well....

The question is how do I best insulate the attic side of an exposed stairwell wall that does not have any significant supporting structure around it?

My initial thought is to create a sort of 2x4 or 2x6 exoskeleton around the sheet rock on the attic side, cover that with plastic or other cheap wrap and fill up the space with blown in cellulose. there is an exterior door from the top of the stairwell into the attic, but was thinking about how to insulate the door as well. maybe glue or screw on some foam panel board?

Also, HVAC is a combined electric heat / ac unit with compartmentalizing dampers that allow 3 zones of heating / cooling in the house. I live in central Arkansas. there are no trees around the house. the west wall is brick, no windows. Its a rectangular house with the longer north / south walls holding most windows.

Incidentally I've found a ton of little mouse tunnels and trails through the blown insulation and although it's really neat to see their little labyrinth of trails, I'm rudely trying to murder them all.

[CowboyAndIndian]

Put some pictures so we can see what you are describing.

[NoCreativity]

Here are some sub par pics of a couple of the walls. These make it look like there are more 2x4s available than there actually are...

[lthenderson]

In my experience, plastic holding blown or loose insulation is a temporary at best solution and a lesson in frustration when the plastic keeps tearing or pulling your fasteners through it. I would just get some bat insulation and staple it to the studs from the attic side.

Edited: After posting my response, I see pictures now posted. The studs appear to be irregularly spaced and if that is the case, I would probably go with 2" rigid foam board cut to fit the spaces and then sealed in with some caulking.

[zolotiyeruki]

You should feel absolutely no guilt about killing mice in your house.  But you also need to make sure to find the locations where they're getting in, and close those up.

I like the suggestion about attaching foam boards.  Personally, I'd attach the foam panels to the framing, then fill the stud bays with blown-in insulation.

[BudgetSlasher]

I would either use foam boards cut to fit, adhesive with foam board adhesive, and sealed at the edges with great stuff or equivalent or explore the option of a DIY closed cell spray foam kit (for bare areas only).   

[soupcxan]

Buy the 24" wide fiberglass batts and cut to fit your irregular widths. If space is wider than 24" then add a 2x4 so you have something to staple the batt to. Then cover the entire wall with 1" polyiso board