The trick to "thermal inertia," and higher R factors working in concert with one another in these "mass wall" systems is "air breaks." So, as an extreme example, say you went through the effort of using cob with a foam core thermal break. You would have to create and "air break" of at least 20 mm (~3/4) between the cob and the foam. These types of spaces can also be enhanced by the application of a "radiant barrier," but the air space in those applications must be "dead air space." With the foam to the outside of the cob mass wall, you will have to vent the air space back into the living space, which is fine to do, as the cob has little R factor to it in the first place, and the foam would then take the brunt of the thermal resistance work for the wall diaphragm. Then the exterior could be clad in wood board, shingle, stone, or a myriad of other systems.
A good friend of mine, living in Minnesota insulated his cob building with wool/lime. So far, it appears to work well with no troubles