Jon, do the calculation, each pillar is the same, so that should pretty easy.
Each face should be taken into account. Xept the floor. As you said.
I have 8 inch thick mass. And it's all right, but heat takes time to travel through it. I don't get any heat coming through for may be two hours after the beginning of the burn.
With your pillar placement, i see two other problems, cleaning. It would be better to have a line of sight from the cleanouts to the opposite wall. And volume.
I mean, for the heat exchange to happen, you need time, surface, and volume. Because if you don't have the volume, you won't have
enough time to exchange heat through the surfaces subjected to heat. Gases will escape the bell too fast.
Remember too, that your system is not ideal. Tall bells are far better. Since there is stratification into those. And way less of the height is occupied by the exhaust side to the chimney.
You can easily get that if 50% of the height is occupied by the exhaust; even tho the gases stratificate in the exhaust too, up to a certain point. The hot gases will have more tendency to escape through that route, than if you have only 10% of the bell's height occupied by the exhaust, at the bottom. Where cooler gases gather.
HTH.