The extractor fan in the clayspace is the wrong kind. It's an axial vent fan. It doesn't develop enough static pressure to pull the fumes out of the kiln.
The best fit would be a 4" axial fan. We could use a 6" fan and adjust some bypass air to get the draw just right. There is a damper on the box under the kiln.
Edit: it needs to be an all metal fan to handle the heat.