High-Density polyethylene (HDPE) and high-density polystyrene (HDPS) can handle high temperatures and could be used for coating your pyrolysis reactor. Also poly-chlorinated (or poly-florinated) polymeric materials can handle such high temperatures.
I would also advise that you put some insulation (foam) between the metallic structural material of the pyrolyzer and the over-wrap layer of HDPE or HDPS.
Polymethylpentene or Polymethyl metha acrylite (PMMA) may be suitable option for your application or you can use double layer or sandwich structure of silica layer with HDPE.
You already answered for the temperature range 400 to 800°C.
As said by Daniel Pawlak, I think that almost no polymeric substance should support long time contact with a pyrolisis reactor working well above 400°C and remaining transparent!
I think you should conceive a different design with other type materials...