There is one way to drill on the drill press and be accurate. It uses the same principle and there used to be a video of it - but the web page has been taken down.
Mark and make a small hole for the entrance and exit points as shown on the video and PDF for the lathe. ON the DP mount a 1/4 to 3/8 inch board, that is about 6 inches square or round, clamp it down. The board needs to have a nail protruding to the top by about 1/8 inch, in the approximate center. Set the antler in place and hold with pliers. Your entrance and exit points are now determeined. Drill down to almost the nail and then raise the antler with the pliers in a similar fashion as in the video on the lathe.
I personally perfer the lathe but if you don't have and MT Drill chuck, this method will work.