Just picking.

The first few runs with the engine will tell more of the related parameters.
After running a few calcs and seeing the result, there is a small chance the gasifier may start weakly pulsing on its own(with a reasonable sized draft pipe).
Either way, the good news is the most friable ash/ember material should be nearest the grate, so whatever (engine) backflow pulse available should hit that area first.
My hunch is that the fuel in the flame tube will muffle the backflow pulse before reaching the inlet pipe. In a perfect world one could almost make the flame tube into a Bodine Reflector(fig.3). Wish someone could explain Bodines lambda notations. Looks like the single tic mark is 1/2 lambda, and the double tic mark maybe a 1/4 lambda?
One background problem is the (engine intake) venturi action for such a large secondary source (1.2" I.D. fuel pipe). In some preliminary pipe"T" testing I notice when the main intake flow starts pulling the secondary flow into the stream, the primary intake air flow is reduced. She will be a "tight rope walk" adjusting the parameters.
Just have to see how it goes.