All of your comments refer to materials and the machine. After operating four different edgebanders over 28 years, my experience is the most common problems are caused by the machine operator making adjustments not fully understood. Since you run a range of materials and thicknesses, I suspect the operator is making adjustments that are compounding the issues.
An experienced and knowledgeable technician needs to fully evaluate the machine to make sure their are no defective components. Then he needs to calibrate and document settings for various banding sizes and thicknesses as well as various materials and thicknesses. The operator(s) need to be trained to use these settings when making changeovers from one material to another. Banding thickness can and does vary from one roll to the next. I experienced this and learned it was a factor in edge quality.
I would then run a large job that uses the same materials and thicknesses to see if issues occur during the run. If so, I would suspect a machine problem still unfound. If none found, I might try another outside technician with fresh eyes. If no issues occur, then I would pay attention to the operators potential introducing issues intentionally or unintentionally.
Edgebanders do multiple simple processes precisely with a variety of materials and sizes. You have a quality machine that should have no problems when properly maintained and operated. Lack of understanding of the mechanics lead to problems.