We present an approximation to the state-interaction approach for matrix product state (MPS) wave functions (MPSSI) in a non-orthogonal molecular orbital basis, first presented by Knecht et al. [J. Chem. Theory Comput., 2016, 28, 5881], that allows for a significant reduction of the computational cost without significantly compromising its accuracy. The approximation is well-suited if the molecular orbital basis is close to orthogonality, and its reliability may be estimated a-priori with a single numerical parameter. For an example of a platinum azide complex, our approximation offers up to 63-fold reduction in computational time compared to the original method for wavefunction overlaps and spin-orbit couplings, while still maintaining numerical accuracy.