ᐅ Breathable exterior insulation, alternative to mineral wool

Good morning,

In addition to the top floor ceiling, I also need to replace the external insulation. Currently, there is 5 cm (2 inches) of fiberglass insulation, with asbestos shingles above it. The shingles are going to be removed, and then new external insulation will be installed. Finally, either plaster or a combination of plaster and wood cladding will be applied, depending on the costs. Since this is a house from 1935 and we do not want to install a mechanical ventilation system afterward, the insulation material should be somewhat vapor-permeable.

The energy consultant recommended 16 cm (6 inches) of stone wool to achieve a U-value below 0.2 and to qualify for KfW/Bafa funding. As we don’t have many windows right now, a relatively thin insulation system is important to me. The thicker the insulation, the more natural light is lost. What alternatives to stone wool could I use to achieve good insulation with a somewhat thinner layer?

Have a nice day,
Heiko