Ice-mass change induces regionally varying patterns of sea-level change due to gravitational, rotational, and deformational (GRD) effects, and these in turn influence marine-based ice stability in Antarctica. For improved projection of the Antarctic Ice Sheet, there is a need for including GRD effects in modeling and improving the understanding of basin-by-basin sensitivity of ice evolution to GRD effects under a range of climate scenarios. We couple a high-resolution, higher-order ice-sheet model with a 1D global sea-level model that fully captures GRD effects, and simulate ice evolution in Antarctica under the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) experiments. We perform two sets of coupled simulations incorporating 1D solid Earth structure suitable for West and East Antarctica and show that the Amundsen Sea Embayment in West Antarctica has the highest sensitivity to GRD effects - in high-emission scenarios, grounding-line retreat accelerates by hundreds of kilometers by 2300 without GRD effects, but GRD effects delay this retreat on a timescale of decades. Yet, we find delay times do not show a clear relationship to the strength of climate forcing alone. Furthermore, GRD effects can influence ice-sheet dynamics more than the choice of climate model for a given emissions scenario. In contrast, East Antarctica exhibits minimal sensitivity to GRD effects throughout the study period. These findings underscore the critical role of GRD effects in shaping future West Antarctic Ice Sheet evolution, highlighting the importance of constraining the regional 3D Earth structure and bed topography in West Antarctica, and particularly the Amundsen Sea Embayment.