My home was originally built as a summer cottage (in Virginia) and therefore has no insulation. It is also not stud wall construction so there is no air space within the wall to fill with insulation.

The exterior is log siding with a vertical post every 4 ft. This post projects out 1-3/4" further than the log siding. I would like to fill this 1-3/4" area with rigid board insulation and/or apply house sheathing over the entire surface and then put up new wood siding over it.

I have been considering either polyiso or FOAMULAR. If I use 2 layers of either of these (the 1-3/4" cavity and the sheathing) do you think I will have a moisture problem where the 2 facers of the 2 layers meet? Since both of these types of insulation are moisture resistant and since there is no vapor barrier on the interior (and no way to apply one now) I think it would be best to let the walls "breathe". Do you agree?

I don't need a perfect wall, just an improvement. I just don't want to create a moisture/mold problem. Any opinions or suggestions would be appreciated.