I must have been getting tired last night. After re-reading it this morning, some things just didn't make good sence ( even to me) with what you originally posted that you wanted to use a HW tank.
Because of it's simplicity, I have really thought about the "S draft stove" , how to make it and what might be needed. A 30 or 40 gallon electric or gas HW tank would lend itself well to this with very little extra material needed if done correctly and the use of a sheet metal break for the bends.
Instead of inserting secondary air into the stove in the back, I would pipe it to the front, heat it and introduce it crossways under the 'smoke shelf' just before the opening. I have thought too that the opening to the top chamber could be much smaller to create a sharp rise in velocity at this point to better mix the unburned/burning gasses with the heated incoming secondary combustion air. The stove area, just after the point of sharp rise in velocity would need to be an expansion chamber where the burned gasses could slow down to give off the most BTUs before exiting in the flue pipe. At least an area with a very high surface area and low relative volume to provide maximum heat exchanger area for the spent gasses.
Anyway, just some thoughts. Use what you like of them, disregard what you don't.