I get to do this with the clocks I repair, for every repairman seems to
mess up the screws that hold the movement into the clock.

The trick I've been using is to (1) gloop a bit of cyanoacrylate glue,
either gel or liquid, onto a toothpick and swish it around in the
afflicted hole, then I (2) remove the toothpick, still wet with glue,
and dip it into a plastic prescription bottle filled with baking soda,
which is an accelerant for this glue.

The toothpick then (3) goes back into the hole where it freezes almost
instantly, and I (4) cut it off with diagonal wire cutters.  A poke
with an awl down the axis of the toothpick opens up a pilot hole.

I've been experimenting with variations on this technique, but this has
worked fairly well so far.  For larger holes I think the bamboo would
work well.

Mark Kinsler
Lancaster, Ohio, USA