Thick toilet paper spindle

This toilet paper spindle (roller, axle, whatever you call it) is designed to fit the core of the toilet paper roll snugly, so that it is centered and rotates smoothly rather than wobbling. In particular, my toilet paper holder is partly inset into the wall, and this prevents the roll from sticking against the bottom and being hard to pull.

You may need to customize it to fit your holder (and spring); I don't know how standard the particular dimensions of these things are. If you do, I recomm