We present (g 475 - z 850) color and z 850-band surface brightness fluctuations (SBFs) measurements for 43 early-type galaxies in the Fornax cluster imaged with the Hubble Space Telescope Advanced Camera for Surveys. These are combined with our earlier measurements for Virgo cluster galaxies to derive a revised, nonlinear calibration of the z 850-band SBF absolute magnitude as a function of (g 475 - z 850) color, valid for the AB color range 0.8 < (g 475 - z 850) < 1.6. In all, we tabulate recalibrated SBF distances for 134 galaxies in Virgo, Fornax, the Virgo W' group, and NGC 4697 in the Virgo Southern Extension. The calibration procedure yields a highly precise relative distance modulus for Fornax with respect to Virgo of (m - M) FV = 0.42 ± 0.03 mag, or a distance ratio dF /dV = 1.214 ± 0.017. The resulting Fornax distance modulus is (m - M)For = 31.51 ± 0.03 ± 0.15 mag, corresponding to dF = 20.0 ± 0.3 ± 1.4 Mpc, where the second set of error bars reflects the total systematic uncertainty from our assumed Virgo distance of 16.5 Mpc. The rms distance scatter for the early-type Fornax cluster galaxies is s d = 0.49+0.11 -0.15 Mpc, or a total line-of-sight depth of 2.0+0.4 -0.6 Mpc, consistent with its compact appearance on the sky. This translates to a depth scatter smaller than the intrinsic, or 'cosmic,' scatter scos in the SBF calibration, unlike the case for the larger Virgo cluster. As a result, we are able to place the first tight constraints on the value of scos. We find scos = 0.06 ± 0.01 mag, with a firm upper limit of scos < 0.08 mag, for the subsample of galaxies with (g 475 - z 850)>1.02, but it is about twice as large for bluer galaxies. We also present an alternative SBF calibration based on the 'fluctuation count' parameter , a proxy for galaxy mass. This gives a consistent relative distance but with larger intrinsic scatter, and we adopt the result from the calibration on (g 475 - z 850) because of its basis in stellar population properties alone. 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.