Hey guys,
Try it this way and see if it isn't better. First, cut enough off the ends of the raw tip to make the ends flat and reasonably parallel with each other. Then hand file a cleanup diameter on the large end of the tip. Locate the center of the small end and center drill it. Place the filed cleanup diameter in the lathe chuck and run a center, live center is preferred, into the center drill hole with your tail stock. Use this set up to rough turn the raw tip at least to a cleanup all the way around. Now place the rough turned tip about half way in the jaws of the chuck of the lathe and drill a spout diameter hole all the way through the tip and run a larger drill, for the correct size tap to the depth needed. Now use a tap wrench, crescent wrench, or an open end wrench to drive the tap into the large diameter drilled hole. (Trying to hand drive the screw tip onto a tap held in the jaws is just senseless.) The tap and tap wrench are held on center by a center in the tail stock. As you tap, go in a couple of turns and back out and then repeat until your tap is at the depth needed. While you have the rough turned tip in the jaws to drill and tap the hole you can also turn the large end of the tip to finished dimension at the same time. Now you turn the tip around to turn it while held on the tap. The largest diameter part of the tip is already turned so that turning the smaller diameters of the tip will put less pressure on the horn tip. To keep the tip from threading deeper into the horn and making it hard to get off the tap when finished, take a regular nut of the same thread size as the tap and saw through the nut from one side into the center of the nut. Screw this split nut onto the tap and then run the tap into the horn tip. Then screw the split nut up snug to the horn tip. This allows you to chuck the tap up short so the majority of the tap is not extended from the chuck jaws. Chuck up on the split nut and run a center in the tail stock into the hole at the small end of the the screw tip. (you already have a hole drilled through the screw tip that is on center with the large end of the screw tip.) Make sure the saw cut in the nut is between two jaws of the chuck. The split nut will keep the tap from going deeper into the horn and make it easy to remove from the tap. If the nut you chose to make a split nut from is not very wide you can make two split nuts and place them a little bit away from each other on the tap. This adds stability to the tap in the chuck. Take it slow and easy when turning the screw tip on the tap.
Randy Hedden