I'd go with epoxy, too, although it would be a bear to reverse if you ever have to. Clean off the stub at the drill, and maybe rough up the hole a little, so you're gluing wood to metal, not old adhesive. And see if one of those rubber bands from a bundle of broccoli closes down enough to work. Almost anything should work, because epoxy is a gap-filling adhesive.
I recently learned - was it from Scott here? - that five-minute epoxy is more flexible than the super-strength stuff, and probably better for this application, since the wood and metal will move differently from each other.
If it fails, send me a private message; I just might - just might - have a suitable replacement.
I sent the student assistant to find the hand drill in my office toolbox once; she returned, telling me it wasn't there. I got to do a little teaching that afternoon!
