Reply by Loren

Chuck the the over long blank into a chuck on your headstock
supporting the other end with a center on the tailstock. Feed
a long drill through the lathe headstock. You may have to make
some sort of apparatus to center the drill in the headstock.

After the hole is drilled to depth, remove the waste piece
from the tailstock end, then remount using the hole as
the center axis and turn the exterior.