How to repair a Lathe tailstock spindle. 2020 10 17

In this video I attempt to repair the quill on my lathe (tailstock spindle). I had an arbor spin in the quill and it left some material embedded in the quill. So I decided to repair it and bought a dremel 3000 to make this repair. My first thought was to grind a stone in the shape of the taper and grind out the material. Photos at the end of the video may contain information not included in the video.