The nonlocal coherent-potential approximation provides a systematic technique for the study of short-range ordering effects in a variety of disordered systems. In its original formulation the technique, however, shows an unwanted dependence on details in the coarse-grained effective medium construction. This is particularly evident in the study of [(k)\vec] -resolved quantities, such as the Bloch spectral function and other non-site-diagonal observables. We remove the issue and recover fully physical results in first principles studies of real materials, by means of a resampling procedure first proposed for model tight-binding Hamiltonians. The prescription is further generalized to the case of complex unit cell compounds, with more than a single sublattice, and illustrated through examples from metallic alloys and disordered local moment simulations of paramagnetism in the prototype iron-based superconductor FeSe.