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The quantum magnet Cu₂OSO₄ exhibits a complex magnetic excitation spectrum whose microscopic origin remains an open challenge in condensed matter physics. In this work, we investigate its magnon dynamics by combining inelastic neutron scattering measurements performed on the CAMEA spectrometer at the Paul Scherrer Institut (PSI) with complementary data collected on the TAIPAN triple-axis spectrometer. Linear spin wave theory (LSWT), implemented using the SpinW framework, is employed to refine a microscopic spin Hamiltonian capable of reproducing both previously analyzed and newly acquired experimental datasets. Three complementary modeling approaches are examined. The baseline model accurately reproduces the historical in-plane dispersion but fails to describe the out-of-plane optical branches observed by TAIPAN. A second model, incorporating a stronger intra-dimer exchange together with geometrically derived Dzyaloshinskii-Moriya interactions, substantially improves the agreement with the TAIPAN measurements while introducing only minor deviations in the planar spectrum. Finally, an effective spin-1 macro-spin description of the copper dimers proves unable to reproduce stable spin-wave excitations, indicating that such a simplified treatment is inadequate. Our findings show that the magnetic behavior of Cu₂OSO₄ arises from a delicate interplay between intra-dimer exchange and the extended magnetic interaction network, providing further insight into the microscopic mechanisms governing its spin dynamics.