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Rigid foam over stucco in a small problem area–worth considering?

meineke | Posted in General Questions on
I’m wondering whether adding exterior rigid foam in a small area is worth doing to help with a problem spot. It’s my first winter in this 1920 Chicago (Zone 5) frame bungalow with 2×4 walls, original sheathing with tar paper, and stucco that has been mostly covered with vinyl siding. The attic and basement are both finished and conditioned; the basement is about 7’6″, with 4′ below grade.
The back wall of the house is attached to an enclosed but unconditioned porch over an exposed crawlspace along about two-thirds the width of the house. The exterior wall under the porch is just stucco; whoever installed the siding didn’t bother there. This also happens to be the coldest spot of the house, a basement guest bathroom.
It seems like it would be a quick, easy job to attach 2″ EPS on the above-grade wall in this area. I’d have to deal with some exterior penetrations, but this area is sheltered and there are no windows, so no flashing (unless I take it all the way to the basement door). 
Is this as feasible as it seems? Would I expect to see any change at all, given that I wouldn’t be insulating below grade or continuing the foam outside this area? It seems the consensus from a similar question was that it would accomplish at least something (
I’m also thinking this is the only way to make any improvement to that cold bathroom without demolishing it; the wall on the interior side (drywall and 2x4s sitting a few inches in from the foundation) has a toilet and tiled shower, so removing it to do proper below-grade foam insulation would be enough work that I’d need to save it for later. Not sure if there is an option I’m not considering, though. The basement is surprisingly dry, no existing major moisture problems to fix. The drywall ceiling blocks my access to the rim joists, so that would also be a larger job.

(please ignore the giant gaping hole for the electrical service–some ancient foam revealed itself to have failed when the first cold snap hit, just waiting until it warms up enough to seal it with the help of a hair dryer)

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