Well, nothing worked.
Finally, I gave up and glued the ends of two lengths of beading thread into either end of the bead. I've probably f'd up whatever value it had, and I feel like a schmuck, but at least I can use it in this necklace. As long as I'm wearing it against a dark background the problem isn't visible. And I made up some custom silver bead caps to protect the ends.

These started life as cigarette holders, I'm told.