I would make a jamb chuck from a piece of wood and reverse chuck the egg (after finishing the other end)
to finish it. I have used this method very successfully. Once I make a wooden jamb chuck for a project I label it to be reused. If you go to www.tnwoodturner.org and click on woodturning online you can then access the projects section. In the projects section there are a couple of tutorials on how to turn eggs including one that details using a wooden chuck to finish the eggs. Good luck!
-- Those that say it can't be done should not interrupt those who are doing it.