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The role played by spin-orbit coupling in the determination of a system's magnetism has recently been the subject of intense study, with particular interest being placed on magnets based on Ru⁴⁺ and Ir⁴⁺, revealing a wealth of novel emergent phenomena. Stemming from the complex interplay of comparable values for J and λ, the parameterization for such phenomena has proven challenging. One particular example corresponds to the modeling of the low energy magnetic fluctuations, where conventional approaches often require complicated phenomenological Hamiltonians. Using the 4d layered antiferromagnet Ca₂RuO₄ as a case study, we demonstrate that a mean-field multilevel spin-orbit exciton model employing a minimalist Hamiltonian captures the main features of the low energy magnetic excitation spectrum. Corresponding to a tetragonally-distorted A-centered antiferromagnetic unit cell, the model accounts for the softening and longitudinal polarization of the Higgs mode. The success of such a minimalist Hamiltonian in capturing such a rich spectrum for a 4d magnet, suggests that the spin-orbit exciton model may be a suitable alternative to traditional approaches.