What if you put the vertical in between the firebox and the horizontal and made it such that you could close off the "left" side of the vertical when in use so the heat did not escape to the horizontal side. Then you could also have a solid "grate" that you could stick in the vertical to cut it off (right near the top of the horizontal) and then the heat would flow into the horizontal if you opened up the wall between them. (obviously you would move the smoke stack to the other side of the horizontal in this scenario).
I'm not an expert on reverse flow, so my suggestion may be completely irrelevant...but the idea popped into my head while looking at the pictures. I have no idea how big you would want everything...