We investigate the cause of spatial superexchange anisotropy in a family of copper-based, quasi-two-dimensional materials with very similar geometries. The compounds in this family differ mainly in their inter-layer separation but they have very different magnetic interactions, even within the basal plane. We use density functional theory and Wannier functions to parameterize two complimentary tight-binding models and show that the superexchange between the Cu2+ ions is dominated by a σ-mediated interaction between hybrid Cu-pyrazine orbitals centered on the copper atoms. We find no correlations between the strength of this exchange interaction and homologous geometric features across the compounds, such as Cu and pyrazine bond lengths and orientations of nearby counterions. We find that the pyrazine tilt angles do not affect the Cu-pyrazine-Cu exchange because the lowest unoccupied molecular orbital on pyrazine is at a very high energy (relative to the frontier orbitals, which are Cu-based). We conclude that careful control of the entire crystal structure, including non-homologous geometric features such as the inter-layer organic ligands, is vital for engineering magnetic properties.