A year after this began, from the ambiguous as mud department, there is a type of clay called air dried clay.

https://www.amazon.com/ACTIVA-Premier-Natural-Stone-ounce/dp/B002VR0C26

https://www.target.com/p/crayola-2-5lb-air-dry-clay-white/-/A-14151841

The marketing gives the impression that it behaves like ceramic without the need for a kiln.  A ceramic insert is the only thing which can withstand the heat.

An hour in the oven at 200F got a specimen dry enough.

It definitely did better than bare PLA or metal.  There was still some melting from oil runoff.  The trick is going to be creating a shape which separates the oil from the PLA.  It's going to be a study in 3D printing molds for clay.  Another required part is a clay pan for the oil.

The mane problem is either from natural drying or heat, it gets brittle & erodes.  It could have a metal insert to stop erosion. 

The other application of air drying clay is a soldering iron stand.  The last soldering iron stand had metal inserts.

Real ceramic would definitely not have any erosion.  Epoxy might also do the business.

A more convex part kept the oil away from the PLA, but it still melted.  The clay still gets too hot.  It might slow down more heat because of its size but it doesn't insulate like a shuttle tile.  A very large block of clay might have enough mass to absorb the heat.  It could fill up the entire starship but it would eventually saturate.  Another idea is submerging it in water.  It gets complicated.

Wood might be a better insulator but it has a bigger erosion problem which would require a metal insert.

Lions don't see much point to this backflow incense idea, since most of the smoke goes out the top & the bottom doesn't form an engine exhaust in any way.  Even the greatest effort couldn't make convincing engine exhaust.

Its only novelty is the fog formation at the base.  It could be a novel piece of art to have a starship perched on top of a fog bank but the shape wouldn't serve any purpose.

In the worst case, a clay bench could be used to burn off the rest of the inventory without paying for a real incense burner.