removing a tailstock taper

[Pete O]

That's a really unusual quill design Andy, I'm with Darren, it appears that it should have a through-hole from the rear- or, as Dr Stan suggested, a slot in the side of the quill, at the depth of the MT2 tool, to accept a wedge-shaped drift. Have you taken the quill all the way out and examined it?
I have a centre that is too short for my tailstock so that the screw doesn't reach to push it out- every time I use it and forget to put something behind it, I get it out by putting an open-end spanner behind the head of the centre and using it as a lever. This will work on any MT2 tool like a drill chuck or a live centre, but is not ideal.
If you do end up needing to modify the quill, I'd be boring a hole from the rear rather than a slot from the side- a drift from the rear could be used with the quill in any position, and even be left in the bore, whereas a wedge would necessitate extending the quill all the way every time.
It would be very strange if there was no facility built into the design for removing the taper though.