The inside of the barrel tumbler needs a polygon (made from wood) in order to (a) give enough “traction” to turn the contents, and (b) protect the barrel from repeated impacts.  I’m going to use Oak or Maple to do this.  Based on the width and thickness of available material, I chose a 9-sided polygon.

Here is a picture of the CAM operation prepared using Fusion 360.   I will make nine of these with just a fraction of an inch extra that I can remove on the jointer while getting a tight fit.