narrower rolls refuse to stay in their slots on each end and keep sliding down on to the rod in the center, preventing the roll from turning—how aggravating!!<<<<
Quick simple fix, might be a big rubber band put on many times so a layer builds up and will hold it.
Liquid Lead will work, to build up new groves, so would a cloth strip, dipped in half Elmer’s glue, wrapped around it many times, allowed to dry and then painted to match your holder.
Try the narrow strip of cloth, plain at first and see if it will work.
Here goes granny telling the engineer how to engineer, go ahead and laugh.
Good ideas, granny. Hadn’t been thinking about solutions, only ranting about the problem. Will try the elastics first-hesitate to use glue as this is an unique holder advertising the E.W.White paper co. of many, many years ago. My family thinks I have completely lost it to become attached to a toilet tissue holder instead of just replacing it.