X-ray spectroscopy of heavily obscured active galactic nuclei (AGN) offers a unique opportunity to study the circumnuclear environment of accreting supermassive black holes. However, individual models describing the obscurer have unique parameter spaces that give distinct parameter posterior distributions when fit to the same data. To assess the impact of model-specific parameter dependencies, we present a case study of the nearby heavily obscured low-luminosity AGN NGC 3982, which has a variety of column density estimations reported in the literature. We fit the same broadband XMM-Newton+NuSTAR spectra of the source with five unique obscuration models and generate posterior parameter distributions for each. By using global parameter exploration, we traverse the full prior-defined parameter space to accurately reproduce complex posterior shapes and inter-parameter degeneracies. The unique model posteriors for the line-of-sight column density are broadly consistent, predicting Compton-thick N-H > 1.5 x 10(24) cm(-2) at the 3 sigma confidence level. The posterior median intrinsic X-ray luminosity in the 2-10 keV band was found to differ substantially, however, with values in the range log L (2-10 keV)/ erg s(-1 )= 40.9-42.1 for the individual models. We additionally show that the posterior distributions for each model occupy unique regions of their respective multidimensional parameter spaces and how such differences can propagate into the inferred properties of the central engine. We conclude by showcasing the improvement in parameter inference attainable with the High Energy X-ray Probe, with its uniquely broad, simultaneous, and high-sensitivity bandpass of 0.2-80 keV.