After building many cob rocket stoves, we were still having the same problem. The cob in the back would not take the abuse of having sticks jammed into it and we couldn't seem to be more gentle.
So I made a -sort of- base out of firebrick and built around it with cob. I built two of them side by side and they are fantastic.
Then I made my boyfriend a T-shirt to wear while he cooked for me. I included a link in case you need one for your rocket chef!