Hold the drill body in a four jaw chuck with copper blocks between the jaws and drill. Indicate at the large end of the taper, fo to small end indicate. Tap till straight. Repeat if required till running true. Dress up center if nicked up. Place live center in tailstock. Have at it. To cut the Taper set up the taper attachment if you've got one before you even start otherwise set compound at appropiate angle making sure the tool is on the center height.
The optimist says the glass is half full, the pessimist says it's half empty. The paranoid in me says somebody put a hole in it.
Remember pessimists are at heart opptomists. They know things can and will get worse.