350 square feet is pretty small - I think a 6" system might be more appropriate to that space. An 8" system would dump a fairly large amount of heat in its burn time, and you would need a larger mass to absorb and moderate it. A 6" system would need a longer burn, but would likely fit the space's heat load better.
A 6" system is recommended to have a maximum of around 35' of duct, and if it was 18" high by 2' wide, that would be something like 100 cubic feet or four cubic yards of cob mix. You could have less and may be good for a smaller space.
The amount of clay compared to sand you would want depends entirely on the character of the clay - is it pure and slippery/stretchy when worked moist, or very gritty and coarse?
My local clay has a lot of sand and gravel in it, and doesn't need much added, but I have seen native clay that was smooth and silty or smooth and sticky.