We have an A-frame house in Alaska.
The ceiling is 2x8 rafters 16" on center with drywall on inside and 5/8" plywood on outside.
We installed R-44 insulation in space, no vapor barrier, no air space. We don't want to remove the plywood since the roof is so steep (slope is 19:12).
Can we install 2x2 furring strips along rafters runs over plastic and resheet with 1/2" plywood to allow air movement and stop moisture buildup on underside of roof deck?
Careful, although you may want an air space, you do NOT want air circulation between your house air and anything on the other side of the vapour barrier. My first thought would be to paint a vapour barrier, such as a shellac based sealer on to your existing ceiling. If your existing ceiling needs re-sheeting, then put up poly, and then re-sheet with drywall.
It's not exactly clear to me what you are proposing. If you are saying you would take off the drywall, pull the insulation out and then build in venting next to the roof plywood, then that would work. Though for my money, if I was going to do that, I would convert to an unvented roof and have somebody shoot a few inches of spray foam next to the ceiling and then put the fiberglass back in. That would give you better performance and no moisture issues.
BuildingScience.com is a great resource for this sort of thing.
Ok, you've created three separate issues here with the construction as you've described it. Any of them, individually, is a large problem. None of them are easily fixable this winter, but the damage shouldn't be too great if you let it go until next warm season.
The first issue that you've created is a lack of a moisture barrier. This matters greatly in your area where you have as great of a temperature gradient between the inside and the outside of the structure. Moisture from the inside of the home (where the relative humidity is generally ~50% for human comfort, higher during periods of cooking or bathing) will migrate through the drywall and any open-celled insulation (fiberglass,
The second issue is that you've created a lack of air movement in the ceiling. This is mostly fine, and is an accepted construction called a "cold ceiling" (more on that in a moment) but combined with your lack of a moisture barrier on the inside, is a critical error. The solution is to either create air movement specifically along the deck of the roof from the eaves to the peak (difficult to create this reliably in a snowy climate), or to install a moisture barrier and to prevent thermal bridging. It's called a "cold ceiling" assembly because you go straight from "cold outside" to "warm inside" without the usual slight insulation properties of the air volume of an attic. Your secondary issue with the cold ceiling is that you have a lot of thermal bridging. Firring, as you've pointed out, will most certainly help with this, but what will help even MORE is putting a several inch layer of EPS foam or Polyurethane foam instead of firring and then putting drywall over that. (You may want to attach firring strips prior to the drywall to ease drywall installation. This is fine.) In fact, you can either kill several birds with one stone, as the EPS can act as a moisture barrier if you spray-foam (with a can) and tuck tape ALL the seams and screw holes.
The third issue is the insulation that you stuffed into that tiny little 8" cavity. R-44 is way too much insulation for that cavity if you used normal fiberglass batts ... You need, last time I looked it up, a 12" space for R-44 to fit. The most you should put in the 8" bay is I think R-26. Fiberglass insulation depends on being 'fluffed' and having air cavities in order to provide the insulation. So you're probably not even getting R-26 out of the R-44 that you have packed into that small of a cavity. If I remember correctly, you need a space 17.5 inches thick to get the full R-44. On top of that, code minimum in your area of the country should be R-49, and you really should have R-60+.
If possible, using your existing materials, I would probably try to find a way to add another four inches to your existing rafters to allow for 12" of space, and then screw 2" of polyurethane foam to it. (Note that you have to use screws with big washers on them to do this.) Run spray foam through the seams, tuck tape the seams and the screws, and you have a 100% airtight construction with a good vapor barrier. Screw the drywall directly to it. Given your climate and the risk of fire plus the risk of smoke from burning polystyrene, I would pay extra to hang 5/8" fire-rated drywall. By my math, you now have R-32 from the batt insulation due to the compression, and then 2 inch panels of polyurethane foam should give you the R-46 that you were going for. Add another 2 inches of polyurethane panels to increase that.
I wouldn't recommend spray foam unless you go all the way with it; a flash-and-batt application here, with or without furring, still means that your moisture barrier would be on the outside of your insulated envelope, which is the wrong place for it, or would create a moisture "Sandwich" if you placed a normal 6-mil plastic vapor barrier on the inside against the drywall. The only proper flash-and-batt application for your climate is an open-cell spray foam on the roof deck, a batt, a moisture barrier, and drywall. Otherwise, you need to specifically get a CLOSED-CELL spray foam, which would allow you to get R-60 in 11 inches of foam plus would create a vapor barrier. Building in a 1.5 inch metal firring channel to your current wood framing and then applying closed cell spray foam up to the attachment surface of the metal channel would solve your thermal bridging problems, your vapor barrier problems, and would get you to R-49.5 or so. Note that you need to use either a hollow metal firring channel or strips of foam insulation and not a wooden firring strip to get rid of the thermal bridging; the metal firring strip also allows you to attach the drywall to it instead of having to hunt through the foam with super-long drywall screws to hang the drywall.
It's fine to do this from the inside. It means tearing down all the drywall, but you are seriously underinsulated for your climate and your building (and health) will suffer for it.
