If you build it the full 3 courses high, it would need a "drop-in" top. It could set on top of the 3rd course but would be shaped like a "u". The bottom of the "u" which is the new roof would need to be down around the top of the second course. Maybe light gauge steel for the sides and the lip, and heavier plate for the bottom.
That exhaust confuses me. What forces all the smoke to even get back that far, to go up and out of the exhaust?