Don,
The #2 taper is the long taper going up into the Quill shaft, the JT taper is the short one attaching the chuck to the long #2 Morse Taper. Did your new chuck come with the long Morse taper? If it did, then, you can replace by removing the whole thing from the Quill shaft. If you are just replacing the chuck ,then you will have to remove the old chuck from the MT and install the new chuck on the old MT.
The Penetrating oil is a good idea to loosen the chuck .It is hard to get penetrating oil to run up hill into the quill shaft though.
To remove the chuck from the Morse Taper, with the jaws open wide, look down inside to see if there is a screw slot or Allen socket to screw off the end of the shaft, Remove the retaining screw and with a large punch drive the Morse taper shaft off the chuck.
On some of the smaller tools the retaining screw inside the chuck is a left hand thread, if the tool is a reversing tool. On the larger tools there is no retaining screw.
Some times the Quill shaft has a slot in it to drive a steel wedge all the way through to remove the #2 Morse Taper and chuck.
Herb