  We present g-z color and z-band surface brightness fluctuations (SBF)
measurements for 43 early-type galaxies in the Fornax cluster imaged with
HST/ACS. These are combined with measurements for Virgo cluster galaxies to
derive a revised, nonlinear calibration of the z-band SBF absolute magnitude as
a function of g-z. In all, we tabulate recalibrated SBF distances for 134
galaxies in Virgo, Fornax, the Virgo W' group, and NGC4697 in the Virgo
Southern Extension. The calibration procedure yields a precise relative
distance modulus for Fornax with respect to Virgo of 0.42+/-0.03 mag, or a
distance ratio 1.214 +/- 0.017. The resulting Fornax distance modulus is 31.51
+/-0.03 +/-0.15 mag, 20.0 +/-0.3 +/-1.4 Mpc, where the second set of error bars
reflects systematic uncertainty from our assumed Virgo distance of 16.5 Mpc.
The rms distance scatter for the early-type Fornax galaxies is
0.49^{+0.11}_{-0.15} Mpc, consistent with its compact appearance on the sky.
This translates to a depth scatter smaller than the intrinsic, or "cosmic",
scatter sigma_cosmic in the SBF calibration, unlike in Virgo. As a result, we
are able to place the first tight constraints on the value of sigma_cosmic,
finding 0.06 +/- 0.01 mag, with a firm upper limit of sigma_cosmic<0.08 mag, at
least for galaxies with g-z>1.02. We also present an alternative SBF
calibration based on the `fluctuation count' parameter Nbar, a proxy for galaxy
mass, which gives a consistent relative distance. Finally, we find no evidence
for systematic trends of the galaxy distances with position or velocity (e.g.,
no current infall); the Fornax cluster appears both compact and well
virialized.[abridged]
