The simplest practical heat resistant holder is a simple toilet seat with the cone taking a dump on metal.  The clay doesn't need to be completely dry but hard enough to do the job.  The toilet seat could be made quite small with some molds.  Its only purpose is to allow the fog to be extracted & free up space for the oil to go.

Then a starship model could be placed around the toilet seat for purposes of wind resistance.  The purpose would be the wind resistance all backflow incense needs, instead of the clear glass cylinder the other burners use.  The very bottom would be open to allow an updraft & fog to come out.