As materials with suppressed ordering temperatures and enhanced ground state entropies, frustrated magnetic oxides are ideal candidates for cryogenic magnetocaloric refrigeration. While previous materials design has focused on tuning the magnetic moments, their interactions, and density of moments on the lattice, there has been relatively little attention to frustrated lattices. Prior theoretical work has shown that the magnetocaloric cooling rate at the saturation field is proportional to a macroscopic number of soft mode excitations that arise due to the classical ground state degeneracy. The number of these modes is directly determined by the geometry of the frustrated lattice. For corner-sharing geometries, the pyrochlore has 50% more modes than the garnet and kagome lattices, whereas the edge-sharing fcc has only a subextensive number of soft modes. Here, we study the role of soft modes in the magnetocaloric effect of four large-spin Gd3+ (L = 0, J = S = 7/2) Heisenberg antiferromagnets on a kagome, garnet, pyrochlore, and fcc lattice down to T = 2 K. By comparing measurements of the magnetic entropy change ∆Sm of these materials at fields up to 9 T with predictions using mean-field theory and Monte Carlo simulations, we are able to understand the relative importance of spin correlations and quantization effects. We observe that tuning the value of the nearest neighbor coupling has a more significant contribution to the magnetocaloric entropy change in the liquid-He cooling regime (2-20 K), rather than tuning the number of soft mode excitations. Our results provide a base for future refrigerant-material design in terms of dimensionality, degree of magnetic frustration, and lattice geometry.