Hi Nico,
My 6” batchbox was in my shop huddled between fixed shelving, a work bench and a wall, all made out of wood. There was maybe a 2” gap between the barrel and metal heat shield, then another 2” gap to the wooden items mentioned behind that.
With the air gap, I was constantly able to monitor the temperature of the wood to make sure it was safe. A general rule of thumb is that if you can’t comfortably hold your hand on the wood (or other flammable surface your trying to protect) then it’s too hot.
It never reached that state so that was good.
Placing a layer of superwool or wall of bricks inside the barrel on the side your trying to protect is a good way to help slow the rate of heat exchange on that side of the barrel for sure. It’s not the type of stove that’s generally burned all day anyway so buildup of heat on this protected side would be far less likely.
Just be sure it doesn’t interfere or restrict with airflow into your manifold or make the barrel removal difficult if you don’t have a removable top for cleaning and inspection.
Are you positioning your barrel so that it’s offset from the riser? Leaving a very small gap between the riser and the barrel on the side you want to protect also helps to encourage the hot air flow to the front where you want it to radiate to.
Having a remote temperature gauge between the wall and the back side of the heat shield would also be a good thing to have and be able to inspect at a glance.
One more thing: if the heat shield was all silver or white (shiny) instead of black, it would help reflect the heat much better... perhaps a negative of your current
art work?