We investigate the use of a regularized optimized effective potential (OEP) energy functional and L-curve procedure [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)] for determining physically meaningful OEPs from arbitrary combinations of finite orbital and potential basis sets. The important issue of the manner in which the optimal regularization parameter is determined from the L-curve perspective is reconsidered with the introduction of a rigorous measure of the quality of the potential generated-that being, the extent to which the Ghosh-Parr exchange energy virial relation is satisfied along the L-curve. This approach yields nearly identical potentials to our previous work employing a minimum derivative condition, however, gives rise to slightly lower exact-exchange total energies. We observe that the ground-state energy and orbital energies obtained from this approach, either with balanced or unbalanced basis sets, yield meaningful potentials and energies which are in good comparison to other (a priori balanced) finite basis OEP calculations and experimental ionization potentials. As such, we believe that the regularized OEP functional approach provides a computationally robust method to address the numerical stability issues of this often ill-posed problem.