I would use straw in the manifold cob, largely for wet strength so it holds its shape well until it stiffens. If the cob gets hot enough near the inner faces (as it surely will) to char the straw there you will get little airspaces which will have a touch of insulating effect (a good thing there).
I think a couple of inches of straw cob around the outside of the mass would be sufficient. The bigger, thicker, or more complex the mass shape, the more straw I would use.
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