I cut a 55 gallon barrel in half and just do an open burn rather than a kiln. I start with a small fire and keep adding material whenever the top of the burn gets ashy. It's easy to quench when it's done because the barrel I used had its bungs sealed, so both halves hold water.

I think the cone shape would work better because I usually have some wood around the bottom edges that doesn't fully pyrolize. But it's easy enough to separate that and add it to the next burn.