Alan Lacer's method
Dennis,
A couple of years ago, I attended a class taught by Alan and Mary Lacer and Andy Barnum, where Alan showed an interesting method (I thought) of doing what you're trying to do.
Put the Morse taper center, mandrel or whatever you have, into the headstock. Using a sharpie, make a mark on the taper showing how far it is inserted into the headstock. Pop the taper out of the headstock.
Take three pieces of rectangular scrap wood, about the length of the Morse taper from the small end to your mark. One piece of wood needs to be a little wider than the other two, to form the base.
On the base piece, place the mark on the morse taper on one narrow end of the base. Align the other two pieces along the length of the taper, on either side. Remove the taper and mark the location of the inside edges of the sides on the base. Now, just glue, screw, or nail the sides in place on the base.
Here's a photo of one I made later out of some scraps of plywood.. it's a hurriedly done picture, but I think you'll get the idea.
It's not a complete female taper, but it's sufficient for you to test the taper you have on your turned element and see if it'll fit.
Hope that helps!
Regards,
Danny