I like the suggestion of creating a rain screen with the 1x1's and sheathing. You have to let the siding dry out and breath. For a residential project at work we have been researching using mineral fiber insulation in the wall cavity of a masonry project. In part due to NFPA 285 and in part for the higher R-value. I wonder if you could use mineral fiber insulation in between the studs. It's non combustible, mold resistant, and can have an R-Value of 4/inch.
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K Burditt AIA
Silver Spring MD -------------------------------------------