This was the money quote in a web page of California Lightweight Pumice I printed a couple of years ago:
"Hardened pumice aggregate concrete has the unique capability of being nailed, sawed or drilled with ordinary hand tools."
This property is related to the bubbles in pumice stopping the propagation of cracks. Seems like this might apply to cracking from thermal, as well as mechanical causes.
I recall reading something to the effect that pumice made a good lining for furnace, kiln, oven, or forge chambers, but the details elude me.
The practice of including horsehair in the clay body for tandoors had me wondering if some carbon fibers might be generated from the horsehair when the tandoor was cured.
With a resistances in series approach to getting the thermal conductivity dialed in, lamination with layers of materials with various thermal and mechanical properties seems hopeful. The monoliths, woodpiles, honeycombs, and foams used in producing catalyst supports offer some interesting, although probably not cheap, approaches to building a core for heat transfer.