Brett,
    Your idea may be worth pursuing--moving the pendulum support horizontally so as to
null the response.  Moving the pendulum support can
emulate a horizontal  acceleration, but it cannot null tilt.  Tilting the case of the instrument would allow to null both ground

acceleration and tilt, but it would require a very powerful actuator--not consistent with a 'noiseless' motor/leadscrew.
    You mention the feedback as a means to improve linearity, but I don't think that is really an issue.
The pole/zero features of the feedback network could presumably morph the short pendulum into an equivalent
long pendulum??  If so, then it would be a means to improve teleseismic sensitivity.  But I don't see any need for
such feedback at really low frequencies.
     A mechanical means for nulling the low-frequency tilt variations would be to move the static plates of the sensor
so as to produce a null output; but this does not influence the dynamics of the pendulum itself.  Thus I don't see it
having any advantage over a high-pass filter with a low corner frequency.  Perhaps you see some advantage to
a combination; i.e., moving both the pivot and the stationary sensor plates (one for short periods, the other
for long periods?) After all, sensitivity is not the show-stopper for hugely long periods when using a displacement sensor whose
electronics desn't wander.
      My guess is that the inherent stability of a feedback system involving a pendulum
would be greater than that of conventional instruments--because of the inherent stability of the pendulum itself.
And I gather that your background in controls is adequate to the task  Physicists are trained in Fourier transform mathematics
instead of the Laplace transform.  I cringe at the thought of this 'old dog' trying to lean that 'new trick'.  I do know a lot
about pendulums, though-maybe having done more experiments of diverse type than anybody else, either alive or dead.  So we might
try to pursue something collectively, if you're interested--and if there is also interest from some student(s) here in pursuing
the matter.  (I work fiarly regularly with engineering majors on senior design projects).

    Randall