Just to update, for those interested, the job is complete. What I did was this:
Used a tiny ball dental burr in my Dremel to start a hole in the center of the broken off shaft. Then, placed it in a vice in my drill press and drilled out the majority of the shaft, leaving a small amount in the threads. Used a tiny EZ-Out to try and remove the rest, which crumbled and came out very easily. I then saw that it was indeed threaded, something like a number 4 or 5 size. I knew my only ivory beads on hand were 6 X 48 so I drilled out the hole to the right size, then re-tapped it to 6 X 48 using a set of taper, plug and bottoming taps which I had on hand, as the NECG ivory bead I had on hand was also that size. Had to shorten the shank on the bead some because it was bottoming out leaving the bead sitting too high on the rib.
Turned out good. Thanks for all the tips and comments.