We recently initiated a search for ultra-compact dwarf galaxies (UCDs) in the Centaurus galaxy cluster (Mieske et al. 2007), resulting in the discovery of 27 compact objects with -12.2<M_V<-10.9 mag. Our overall survey completeness was 15-20% within 120 kpc projected clustercentric distance. In order to better constrain the luminosity distribution of the brightest UCDs in Centaurus, we continue our search by substantially improving our survey completeness specifically in the regime M_V<-12 mag (V_0<21.3 mag). Using VIMOS at the VLT, we obtain low-resolution spectra of 400 compact objects with 19.3<V_0<21.3 mag (-14<M_V<-12 mag at the Centaurus distance) in the central 25 of the Centaurus cluster, which corresponds to a projected radius of ~150 kpc. Our survey yields complete area coverage within ~120 kpc. For 94% of the sources included in the masks we successfully measure a redshift. Due to incompleteness in the slit assignment, our final completeness in the area surveyed is 52%. Among our targets we find three new UCDs in the magnitude range -12.2<M_V<-12 mag, hence at the faint limit of our survey. One of them is covered by archival HST WFPC2 imaging, yielding a size estimate of r_h <= 8-9 pc. At 95% confidence we can reject the hypothesis that in the area surveyed there are more than 2 massive UCDs with M_V<-12.2 mag and r_eff <=70 pc. Our survey hence confirms the extreme rareness of massive UCDs. We find that the radial distributions of Centaurus and Fornax UCDs with respect to their host clusters centers agree within the 2 sigma level.