Ted,
    The reason for replacing the upper long piece of your system with a
concentrated mass close to the axis is to increase the Q.  This involves
two factors: (i) more air to move with the long piece, and (ii) the
flexure of the long upper piece gives rise to increased internal
friction damping.  Yes, go as long as convenient for the bottom part.
Of course, lengthening the bottom section requires either an increase in
the size of the upper mass--or some upper movement to get the desired 20
s period.
  The pendulum will be nearly balanced, as you note, with the center of
mass being very, very close to, but slightly below the axis.  To dampen
the pendulum would negate the very thing being sought; i.e, the greater
sensitivity because of a large Q.
     An estimate for the Q can be easily managed as follows.  Disturb
the pendulum and count the number of cycles until it has decayed to 37%
of the initial amplitude.  Dividing this number by 3.14 gives the Q
value.  I doubt that you will be able to get a Q bigger than about 40
with common materials.  The use of materials like a carbon-fiber arrow
(archery) for the lower part should work fairly well.  You might also be
able to just rest the upper mass on a flat-top-piece holding the axis,
without securing it.  Insofar as axes are concerned, I have used
ball-point pen tips on sapphire (or even glass) to provide a decent
axis.
   Good luck with it,
Randall