My 1942 Sebastian lathe has a Morse Taper 3 tailstock. It came with a MT 3 live center with no tang. I am using a MT3 chuck off my Harbor Freight drill press to drill center holes in the end of stock for the live center. The chuck has a tang. When I unscrew the tailstock all the way back it is difficult to get the live center out. The MT3 chuck pops right out. I have cleaned the live center arbor with a steel brush on a grinder and lubed it well. Do I need a MT3 arbor with a tang or is my taper just out of spec? Thanks.