The first implementation of a recently introduced method based on the extraction of the coordination dependence of surface bond-energy variations (CBEV) from density-functional theory (DFT) computed pure-metal surface-energy anisotropy is reported. In particular, polynomial functions fitted to DFT data computed previously for Pt, Pd, and Rh are used as input energetics for statistical-mechanical computations of Pt-Pd 923-atom cuboctahedron-cluster compositional structures (and Pt-Rh(111) as a test case) using the free-energy concentration expansion method (FCEM). The major findings concern the roles of preferential strengthening of intrasurface and surface-subsurface interlayer bonds leading to quite unique segregation characteristics: (i) strong Pt segregation at certain (111) surface sites of the Pt-Pd clusters, accompanied, at relatively high overall Pt composition, by weaker Pt segregation forming Pt-Pd ordered (100) structure, whereas Pd segregates mainly at the edge and vertex sites; (ii) dominant Pd subsurface segregation. The high computation efficiency of the CBEV/FCEM approach allows the determination of the complete temperature dependence of atomic-exchange processes among surface sites, as well as between subsurface and deeper sites, reflected in the corresponding configurational heat-capacity curves. Compared to other approaches, the high transparency of this method helps to elucidate the origin of the distinct bond-energy-variation effects on site-specific segregation in alloy nanoclusters.