For a closer validation of four-component relativistic DFT methods within the matrix Dirac-ohn-Sham (mDKS) framework with global hybrid functionals for EPR parameter calculations to be applied in the modeling of tungsten enzymes, we refine a previously suggested protocol for computations on 5d systems. This is done for a series of larger, unsymmetrical W(V) complexes thought to closely resemble enzyme active sites in this oxidation state. Particular focus is placed on complexes with thiolate and dithiolene ligands, along with an evaluation of the influence of different amounts of exact-exchange incorporated in hybrid PBEO-xHF functionals, an implicit solvent model, and structural changes on the computed EPR parameters. Compared to previous work, a slightly modified protocol with different optimal exact-exchange admixtures for electronic g- and hyperfine A-tensors is found to provide the best agreement with experimental EPR data. It will provide the basis for our subsequent tungsten enzyme modeling efforts.