North America experienced a total solar eclipse in April 2024, offering a rare opportunity for coordinated observations of the solar corona. This study draws from a vast collaborative campaign that combined ground-based, airborne, and space-based instruments, and supporting modeling efforts. Our multi-observatory dataset, spanning a broad range of wavelengths and spatial scales, to evaluate and refine diagnostic methods for inferring key coronal plasma parameters. In particular, we assess the reliability of density measurements by comparing outcomes from distinct inference approaches, and we demonstrate that the accuracy of non-thermal line-width determinations can be enhanced by incorporating additional readily-available physical constraints. We further examine the assumptions and limitations inherent in these diagnostic techniques. Robust analysis remains essential for extracting the full scientific value of coronal observations. These results underscore the coronal potential of DKIST and UCoMP, to advance coronal plasma diagnostics, and provides methodologies that are readily applicable to future observational analyses.