Thanks for the update. I LOVE reports after a full heating season, so much more useful than baby pictures without follow-up!
With the clay slip mortar: Yes, it should be very thin.
We usually support around the firebox by layers of other masonry that double- or triple-seals. Perlite mixed with a very little wet clay so it doesn't move (maybe 2 gallons of liquidy clay-slip, like thick paint, for 2 cubic feet of perlite).
Then a good layer of cob about 4" thick, or a second layer of brick with tidy, airtight mortar.
You need a little room around the firebox for thermal expansion (perlite mixed as above seems to provide this, though the bricks can shift slightly over years. Or you could do a ceramic-fiber fire insulation blanket if you can get it). But if it is too unsupported, handling the wood will loosen the bricks, and loose materials like perlite or sand can flow into small cracks and make them bigger.
Bricks expand with heat. cracks move. bricks cool and shrink. more sand gets in. Iterative self-destruction of firebox.
Include expansion joints (room for firebox bricks to expand), and don't back firebox with loose fill unless it is big enough particle size to stay out of cracks. The expansion joints create a 'floating' firebox that can move slightly, independent of the cooler masonry surrounding it. You may only need a little bit of fiberglass gasket between the firebox bricks and the cooler masonry, but you will need something if you want it to stay airtight. Which you definitely do.
I like this overall design, it is not a bad idea since you want the heat to go upward in the basement.
But since it reverses the placement of masonry (around the firebox) and bare metal (the later barrel), the fire performance may not be exactly comparable to the more common J-style with bare metal around the firebox. I would like to find out more from people using this masonry bell around the heat riser, to see how close they come to the same fire function and output temperatures. But until you seal up the cracks in the firebox, it's not exactly a fair test.
In contemplating the batch box - remember that the door is a CRITICAL component of a batch box. If it is not the right size, and particularly with the right air feeds, the batch box does not burn clean.
A leaky batch box, or box whose door is working loose and leaking, would also not be expected to burn clean.
Dirty burn and heat extraction = creosote = risk of chimney fires and really obnoxious cleaning bills.
A good door, and the metal hardware to support the door without shifting the masonry as it is used and abused, is not cheap and easy to add after building everything else. It has to be planned, with appropriate provisions for thermal expansion (metal expands more than masonry at the same temperature but metal outside the firebox may be a lower temperature than the bricks..... it's worth looking at good oven door framing, or a successful masonry heater design that you can see construction pictures, to see how to hang these doors and how to incorporate expansion joints so the metal and masonry can have a long and happy marriage).
We have done a lot of J-style
heaters because we can shut them down with a couple of bricks on top, which is a $4 solution instead of a $400 solution. I aspire one day to be able to do nice tight metal doors without being intimidated, but for now, I consider it a non-trivial concern when choosing a heater style.
However, it seems to be non-trivial for inspectors too - a nice pretty door instead of a couple of bricks can go a long way to convincing official types that it's a "proper" masonry heater. All the clearance rules are written for vertical openings, not horizontal holes in the floor. Sigh.
Please keep posting if you do another iteration!