Charles,
     Yours is a splendid idea!  Except we need to avoid rolling components because of their 'killer' friction.  I view the
application of your idea as follows.  Imagine the (primary) pendulum axis to be at the top of a rod that is being driven at its
bottom like an inverted (secondary) pendulum by a feedback network.  If the length of this secondary pendulum is carefully
selected, and its motion is phase-matched to that of the primary pendulum--then as you say, the effective period can be much
longer than that of the primary pendulum swinging from a fixed support..  Of course the arrangement will not work without
feedback; however, the feedback should allow the the short pendulum to be morphed into an equivalent longer pendulum.
Voila--increased sensitivity!
    Randall.