How about a slow, small, hot fire. My thinking is to minimize the amount of plant material that goes up in smoke, making a fire that produces the least amount of visible smoke the most productive. This might not give you the greatest volume of ashes, but hopefully it will minimize the amount of potassium that gets carried away.
Use a TLUD gasifier but instead of quenching allow things tk burn down to ashes, I've seen what I suspect to be potassium salts (greenish and pink) when I did this using carob pods as feedstock.
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A century or so ago, ships came from Europe, chopped and burned massive volumes of wood into ashes, and took them home as a highly valuable cargo. Potash!
You can thank my dental hygienist for my untimely aliveness. So tiny: