Thanks to all for the emails and contributions.  This group has the
best and most helpful people!  My problem was much smaller than I
thought and the solution was actually the simplest.

I went to an auto parts store asking for an "Easy-Out".  Unfortunately,
they speak only Hebrew and didn't know the part which was described
here (as I didn't) and they sold me a simple screwdriver with a kind
of spring which grabs the screw.  It's  usually intended to place a
screw when it's difficult to get it into its hole.  Somehow, this
spring managed to catch on the screw and it came down, unbent, unharmed
and unstripped.

When I next move it, I will take a moment to glue a dowel in the hole,
drill out a set hole for it and replace the original screw.

Regards and thanks,

Eliyahu Shahar