Widely employed Near-Edge X-Ray Absorption Fine Structure (NEXAFS) spectroscopy probes a system by excitation of core electrons to unoccupied states. A variety of different methodologies are available to simulate corresponding spectra from first-principles. Core-level occupation constraints within ground-state Density-Functional Theory represent a numerically most efficient means to this end that provides access to large systems, examples being surface adsorption, proteins, polymers, liquids, and buried, condensed phase interfaces (e.g., solid-liquid and solid-solid). Here, we systematically investigate the performance of different realizations of this approximate approach through the simulation of K-edge NEXAFS-spectra of a set of carbon and nitrogen-containing organic molecules. Variational collapse to the ground state and oscillatory convergence are the major complications of these approximate computational protocols. We present a modified version of the maximum-overlap method to achieve a self-consistent inclusion of electrons in virtual states for systems where convergence is hampered due to degeneracies. Our results demonstrate that reliable spectra allowing for a semi-quantitative analysis of experimental data are already obtained at the semi-local level of density functionals and with standard numeric atomic orbital basis sets.