I am still not taking off enough towards the base.
Still, while I have support at the bottom I sand the interior with the lathe off, going in as far as I can with a disk.
As I am sanding I taper the wings to a finer edge. Sand paper is a cutting tool, especially in the coarser grits.
but not the inner. One more cut would have made the difference. It is not necessary for the nail to be there but it does add a point of interest. It also indicates that a line of nails around a vase in a pattern could be a possibility in the future.