You can turn the taper with a manual lathe. You need an expanding mandrel dead center and live center. We made the dead center by simply turning a piece or round stock in the chuck or collet to a 60* point. the mandrel sits between the centers with tension to grip the centers ( a small lathe dog can be used to drive but for light turning isn't necessary) and the tailstock is offset to the desired taper. The machine then turns the taper using the carriage and feed. The pain to this is resetting the tail stock back to zero when done.