I fully agree with using a bell instead of a piped mass. I do think that with your climate and likely intermittent or light heating requirements, a J-tube would be quite practical, and easy for a novice to build. With the core and riser in the location you show, you can build a single-skin brick bell to clear the riser and have enough space to the stairs above to be safe. (I would not feel safe with a barrel under the stairs at all.)
I would consider a narrow tall bell (just big enough for good airflow around the riser) with a bench-height extension to the left. This would all need to be sized for the right internal surface area.
Batchrocket.eu gives the complete information on this; an 8" J-tube has been found to be similar to a 6" batch box for bell sizing purposes. If you can exit nearly straight up, I believe a 6" chimney will serve you well. An 8" chimney would be bigger than you need, and you would have lazy exhaust and possible condensation issues. I would not be concerned about oversizing a J-tube, as you can burn just one load a day if your heat needs are slight, and not overheat the house.
The stair location looks ideal for evenly heating your house.
For structural support, I would suggest adding a couple of posts between the existing ones under the bell, to equalize the loading. I also like your idea of making the mass exposed on the bedroom side.