In this work we have explored the impact of various approximations in spin-phonon coupling calculations of the magnetic relaxation dynamics for a single-molecule magnet in the crystalline phase. We have shown that considering the solid-state phonons, as opposed to gasphase vibrations, along with a dense sampling of reciprocal space, is crucial. We have also shown that significant errors arise in the electronic-structure calculations when employing finite crystalline slabs due to the presence of unphysical surface charges, but that this can be corrected by employing a perfect conductor screening model, which is compatible with our existing methods for accurate and efficient calculation of spin-phonon coupling constants.