Just another thought:
You could try and match the taper on the chuck to the taper in the spindle most are not really hardened. Transfer the contact areas by marking the taper with sharpie, chuck in a lathe, alter taper by taking off a little on the big side, check fit with sharpie, repeat as necesary. Not an extensive description, I am assuming you have access to a metalworking lathe, and know how to turn tapers.
It would produce a non-standard but fitting taper without special tools.

Peter