Backer board does not seem to have much of an advantage. Check your floor structure, make sure it is strong
enough first. Plastic would be my choice, keep the moisture out of the framing/floor. This will need enough cob to protect the plastic from heat of
course. The small
greenhouse I am working on will have a 55 gallon drum cobbed onto the top of the woodstove - a copper coil will sit in the open vat, a pump will move the heat through pex into the soil. The drum boiler will keep the humidity adjusted in the
greenhouse. Going to use the cob and some chimney tile around the drum to channel the flue gas around the barrel. Cob is a great material to use around woodstoves.