Hi Carl, I agree with Glenn and Thomas for most of their comments. The batchrocket is developed with a real bell in mind, not switchbacks like the old-fashioned Russian stoves used to be made. This was done in such a way that the top could be closed with the same large bricks they used for everything else.
But the Russians from 2 centuries and more ago didn't build a batchrocket as the combustion core. The main difference: the batchrocket design is a very powerful combustor, it'll produce an enormous amount of heat in a relatively short time frame. And because of this rocket-type behaviour, there's lots of gas expansion in the bell's cavity. Every change of direction of the gas stream is friction, let alone pinched areas from one cavity to another like your mock-up shows. If there is one characteristic which every batchrocket is showing: they are very, very picky about friction in the smoke path. Even when it don't look like that, it will play up nevertheless when the thing is running full bore.
Besides that, your construction means starting it in fall every year will be a bitter fight before it will play ball.
Please consider a large single bell, no switchbacks of any kind. In case you want to build a smaller bell and a bench beside, treat these as one single bell. To this end, the bench
should be completely open to the bell, in fact the opening between bell and bench should be as large as the entire inside of the bench, i.e. the height and depth of it. Even a 2" high lintel construction that is lower than the bench' seat inside, will hamper the gas stream big time. I've experienced this phenomenon twice, in two different
heaters, before it dawned on me what caused it to malfunction.
As a note: it isn't enough to use firebricks on flat for the top end of the bell. The gases will get very hot in there with a fat chance that the expansion/contracting cycle will drive the bricks apart. Best construction to date for a single walled bell is the one done like the Mallorca build. See
https://batchrocket.eu/en/designs#squarecore
All wall higher than the riser, bricks on edge, a layer of 1/2"
superwool and split firebricks as the inside liner. This way, the firebricks are allowed to expand without cracking the red bricks outer layer apart.
In case you want to have more mass, make the whole bell double walled and you will be surprised at the amount of bricks that will go in there!
Having said all that, it's your house, your heater. If you want to try untrodden territory instead of tried and proven methods, please go ahead.