I use a full-size Union Graduate lathe for all handles and glue the rings directly to the blank. Chucking up the whole butt section is not a problem and the final turning and sanding is the final turning and sanding. I find it is a far cleaner and more precise process. The ability to use a skew in shear allows far faster removal of the excess cork with far less dust in the air.

Rigging it with drill presses and such is not impossible, but it can complicate things.