Hi Justin;
I do know a few things about Matt's stoves. They are not a J tube design. Nor are they a Peter Berg batch box design. Although closer to a batch than a J tube.
Matt's stoves are built with ceramic fiber board throughout. Surrounded by red clay brick. So they lose no combustion heat when starting or running. Every btu is traveling towards the chimney.
I do know that his stoves use a bypass startup arrangement to heat the vertical chimney, prier to heating the oven and or mass.
So your not so horrible drawing. Your showing it in a J design. Matt's riserless is not a J. You have your exhaust turning 180 degrees and then again 90 more degrees. At that point you have slowed the gasses down considerably. Draw will not be nearly as good as it would in a conventional J tube with one 90 degree turn. Flow thru a horizontal mass will also be compromised, how much is the question...
If a rocket stove loses draw then it all starts flowing backwards... into your building.
So having told you all that. We call ourselves rocket scientists , we learn by experimenting. If you are determined ,then give it a try. Just be prepared for it to be "finicky at best and belch smoke /fire into your house at the worst .
I am curious where you are trying to put a
rmh in only 36" of room?
No, your thinking is not flawed about heat rising. It does have a limit and it will stall.