Print a pair of these to clip onto your slatted shelves and hand the paper towel roll from.
Designed to clip onto a 16.5mm slatted shelf, tube diameter of 42mm, with clearance for a jumbo roll with about 56mm of clearance.
Dimensions included in the images.
I also used a rubber band between the two clips just to hold them together on the shelf. It's not really needed unless you have some serious spillage you want to mop up, and are going hell for leather on the paper towels.
Printed with no infill, end result is quite flexible. Use infill for a more robust part if required.