Brendan, word of caution, straight away.
"ciment fondu" i used because of the lack of translation. It's a dark clayey concrete, that we have in France. But in other parts of the world too. And often called ciment fondu. It is refractory.
Well, if you want portable. Keep what you have.
What is that pile of crushed stuff behind the tiles? If anything made out of red clay, you have a wonderful "grog" or "chamotte" ( kind of sand made out of already fired clay elements, which have been crushed. Easy to do) nearly ready on hand. If you can't find clay, use ciment fondu. I'm pretty sure there's a supplier near you. Mix the red clay debris, which have already been fired once, with either clay or ciment fondu. To make a batch, with your vertical pipe from the J tube as a mold, sacrificial piece. Which will die. But in a long time, since it's stainless steel. I would make a shelf, lower than your pieces of flat iron you used to brace the feet. To hold the batch.
Make parts for your batch firebox, out of that grog and binder (again, clay or ciment fondu) Either flat pieces, that you will hold with wire. Or something more refined, like Peter's castings.
Myself, i build out of whatever flat pieces i can find, like pizza oven slabs.
Then insulate the "core" (heat riser and firebox) with either rockwool, glass fiber insulation, or
superwool. Stay away from the real ceramic felts/wools, as they are dangerous for your lungs. Hold the insulation with chicken wire or something alike.
If you want portable. I would just move the chimney to the very front. Over the mouth even. And insulate the arch. I would do this with the compressed rockwool we have here, and a piece of sheet metal. Shaping the two like the insides of the barrel, shoving it in somehow (cut the barrel at the back, and reassemble after, either welding or riveting) And hold the two in place with bolts through the two layers and the barrel. Thought, there is many other ways.