Just thinking off the top of my head, but why not buy a cheapo off-the-shelf toilet paper roll assembly for its dowel and modify it to fit your needs?
Take it apart, and using the end with the spring-action in it, mount it to the end of a wood dowel of the proper diameter (so the dowel fits inside loosely and can slide against the spring) and of course, the length you need.
May not be the best looking, but some paint on the plastic/metal part should make it look OK... besides, the paper towel roll always covers it up.