We have extended the search for luminous (M_{b_J} <= -10.5) compact stellar systems (CSSs) in the Virgo and Fornax galaxy clusters by targeting with the recently commissioned AAOmega spectrograph three cluster environments -- the cluster cores around M87 and NGC 1399, intracluster space, and a major galaxy merger site (NGC 1316). We have significantly increased the number of redshift-confirmed CSSs in the Virgo cluster core and located three Virgo intracluster globular clusters (IGCs) at a large distance from M87 (154-173 arcmin or ~750-850 kpc) -- the first isolated IGCs to be redshift-confirmed. We estimate luminous CSS populations in each cluster environment, and compare their kinematic and photometric properties. We find that (1) the estimated luminous CSS population in the Virgo cluster core is half of that in Fornax, possibly reflecting the more relaxed dynamical status of the latter; (2) in both clusters the luminous CSS velocity dispersions are less than those of the cD galaxy GC system or cluster dE galaxies, suggesting luminous CSSs have less energetic orbits; (3) Fornax has a sub-population of cluster core luminous CSSs that are redder and presumably more metal-rich than those found in Virgo; (4) no luminous CSSs were found in a 10-20 arcmin (60-130 kpc) radial arc east of the 3 Gyr old NGC 1316 galaxy merger remnant or in the adjacent intracluster region, implying that any luminous CSSs created in the galaxy merger have not been widely dispersed.