Brainstorm with me: making this into a better rocket stove?

I'm taking a welding class, and our next project is to make a K-type rocket stove. (I can't really change the design)

Now my understanding is that this is not a true rocket stove, because it lacks insulation. But let's say I were to build some sort of enclosure for it?

My first reflex is to make this into a miniature rocket mass heater. I have clay, sand and straw, so I could mix up a cob mixture and wrap the whole thing up? Is that completely insane?

Would it improve the burn, or is the K shape inherently less efficient because of the lack of an horizontal chamber?

It could be done of course, but then the regular steel will deteriorate even faster, because the heat transfer to the outside will be slowed down. If it was made from some high nickel alloy it could last. I would do the opposite: make the core from clay/bricks and encapsulate in steel armor.