It is virtually certain that Antarctica's contribution to sea-level rise will increase with future warming, although competing mass balance processes hamper accurate quantification of the exact magnitudes. Today, ocean-induced melting underneath the floating ice shelves dominates mass losses, but melting at the surface will gain importance as global warming continues. Meltwater at the ice surface has crucial implications for the ice sheet's stability, as it increases the risk of hydrofracturing and ice-shelf collapse that could cause enhanced glacier outflow into the ocean. Simultaneously, positive feedbacks between ice and atmosphere can accelerate mass losses and increase the ice sheet's sensitivity to warming. However, due to long response times, it may take hundreds to thousands of years until the ice sheet fully adjusts to the environmental changes. Therefore, ice-sheet model simulations must be computationally fast and capture the relevant feedbacks, including the ones at the ice-atmosphere interface. Here we use the novel surface melt module dEBM-simple (a slightly modified version of the "simple"diurnal Energy Balance Model) coupled to the Parallel Ice Sheet Model (PISM, together referred to as PISM-dEBM-simple) to estimate the impact of 21st-century atmospheric warming on Antarctic surface melt and ice dynamics. As an enhancement compared to the widely adopted positive degree-day (PDD) scheme, dEBM-simple includes an implicit diurnal cycle and computes melt not only from the temperature, but also from the influence of solar radiation and changes in ice albedo, thus accounting for the melt-albedo feedback. We calibrate PISM-dEBM-simple to reproduce historical and present-day Antarctic surface melt rates given by the regional atmospheric climate model RACMO2.3p2 and use the calibrated model to assess the range of possible future surface melt trajectories under Shared Socioeconomic Pathway SSP5-8.5 warming projections until the year 2100. To investigate the committed impacts of the enhanced surface melting on the ice-sheet dynamics, we extend the simulations under fixed climatological conditions until the ice sheet has reached a state close to equilibrium with its environment. Our findings reveal a substantial surface-melt-induced speed-up in ice flow associated with large-scale elevation reductions in sensitive ice-sheet regions, underscoring the critical role of self-reinforcing ice-sheet-atmosphere feedbacks in future mass losses and sea-level contribution from the Antarctic Ice Sheet on centennial to millennial timescales.