Breathable construction is your friend, if you have solid stone walls. Gas diffusion through solid materials is significant. Also insulations like woodfibre, covered with dense vapour-permeable sheets such as clay boards are brilliant as they not only provide thermal mass and insulation, but act as a moisture buffer. Dampness is absorbed at periods of high humidity and released as the vapour gradient changes. It might be a long shot as the single form of protection in a draughty garage, but if you're insulating already then it'll certainly be a great help to a dehumidifier. This humidity buffering technique is a common alternative in Europe to the ceramic tiles we like over here in bathrooms, as condensation is drastically reduced.