I really haven't read all the replies and I don't think I need to....
Foggy, you are talking to the 
boys and 
not SWMBO... buy that bigger lathe or at least a 
chuck/cole-jaws that will fit.
Now if I loaned you my bigger lathe and all my chucks, I'd probably have to try this way,
    
    
along with a prayer to the wood nymphs.
I would be drilling with a 
9.525mm Viking Norseman Vortex Point Step Drill Bits (to be reviewed so I'm leaving the links/close-ups to 
'ron).
 
 
    
    If your first cut is too short... Take the second cut from the longer end... LBD