Yes, it would work. But there's no need to let the gases go up and down twice, one time will do the trick. Change in the direction of the gases pose friction so you'd better to do that sparingly.
I think what you mean by a gap of 1" is the top gap, the opening between the end of the riser and the top of that brick "barrel"?
The right way to do this is to replace the barrel by a completely brick surrounding, preferably quite a bit larger than the barrel itself. The bricks will extract the heat slower so you need more surface area to do the same. In fact, when it's large
enough this will act as a masonry bell heater, the combustion core being a rocket heater in this case.
About the top gap: unless you want to cook on the top, you can make that actually as large as is practical. Years ago, I tried to find the maximum distance between the riser and the top in an entirely brick setup. The ceiling of my
workshop limited the top gap to 4 ft and the thing kept working without any sign of hesitation. One remark though: this experiment was coupled to an adequate chimney. Without that, it wouldn't work but that goes for most of the rocket
heaters I've worked with of whatever construction.
See
this link for the brick experiments.