Mark, I drill all my horns by hand, cut off the tip, mark the center and drill away, I do not use a pilot hole just a 1/4" bit.
Then I work the horn down as the tip gets closer to the size I'm looking for I make the tip, sometimes I already have tips made and start working the tip onto the horn. I taper the tip and the horn, once the tip is close and the horn is final shaped I finish fitting the tip, rub pencil inside the tip and press it on the horn, then remove the transfer until I get a good fit. Notice the end of the horn is flat as is the inside of the tip, not sure that is necessary just the way I do it.Once every thing is ready to go together I put a 1/4" rod through the tip and into the horn, that usually takes care of it. The rod also works as a stop while drilling the holes for the pins and while the glue dries if your using any. Be sure and put a thin coating of wax or Vaseline on the rod so it stays free.
A couple pix, the tool that I use to taper the inside of the tip is an old 3/4" pipe reamer that I broke off.
Hope that helps.
Tim