This study proposes an advancement of the three-phase two-point Material Point Method (MPM) with stabilization and boundary enforcement techniques. The governing equations adopt accelerations of the solid skeleton, water, and air phases as primary unknowns, allowing the consideration of high-frequency interactions. The two-point discretization treats solid and fluid phases with separate sets of material points, enabling accurate tracking of their large relative motion. The formulation addresses key numerical challenges in multiphase analyses by incorporating strategies that mitigate velocity interpolation noise, reduce cell-crossing errors associated with anti-locking procedures, and enable robust imposition of potential seepage boundaries at unsaturated surfaces. These improvements aim to enhance stability and physical consistency in scenarios involving liquefaction and extreme strains. Validation is conducted through dynamic centrifuge model tests of embankments over liquefiable soils at 50g. Numerical simulations reproduce key experimental observations, including excess pore pressure build-up, liquefaction onset, and post-liquefaction settlement. Crest settlement histories and pore pressure responses show reasonable agreement with measurements, while sensitivity analyses reveal the influence of damping parameters on deformation trends. These comparisons confirm the capability of the proposed framework to capture complex hydromechanical interactions under seismic loading. These findings highlight the potential of advanced MPM formulations as a reliable tool for geotechnical earthquake engineering, bridging the gap between physical modeling and large-scale numerical simulation.