I am so sorry. I totally missed the objective with the barbie. For some reason, I read "wall" and went from there. Give credit to increasing, things go fly right by more than they used to, and I really love southwest architecture where I had seen walls constructed the way I mentioned in the diatribe.
THEREFORE, I would bring up the construction of outdoor "pizza" style ovens as my only reference. This may have some interest for you. Infact, I would like to have one myself cuz you can do anything in them, roast the beast, bake bread and pizza, bar-b-que, etc. You know the style, Bee Hive and all that. Perhaps the details of their construction would be helpful. I used to have the site in "Favorites" but don't anymore. Gave up for the time being. But, try key-wording "ovens,pizza" and I think you will get it. The detail that strikes me was how they created and insulated the "oven base" with sand and concrete........a "sandwich", if you can stand the pun.........in their kits. These kits are for indoor or outdoor use.........like you see in cool pizzerias. Could be helpful for another idea or two.
Again, I am sorry for going the wrong direction, amigo. Good luck. BEG