We critically examine the algorithmic framework for estimating spectral densities using the Hansen-Lupo-Tantalo method. Our novel approach enables the extraction of various physical quantities, including both on-shell observables such as lattice gauge theory spectra and off-shell quantities as matrix elements linked to specific interpolating fields. As a case study, we focus on symplectic gauge theories with a mixed fermion representation, incorporating both fundamental and two-index antisymmetric fields. We comprehensively discuss potential systematic effects and benchmark the results from spectral density methods against traditional data analysis approaches, including the generalized eigenvalue problem and correlation function fitting techniques. Our algorithm and code can be also applied to theories with alternative gauge groups and matter field content.