The rapid advancement of high-speed railway (HSR) has imposed significantly higher demands on rail tracks' performance and vibration mitigation capabilities, necessitating the design of track systems that can withstand extreme operational conditions while ensuring passenger comfort. Precast epoxy asphalt-cured track (PEACT) has emerged as a promising solution, offering superior mechanical properties and environmental adaptability. In this study, a full-scale finite-element model of PEACT is established and validated. Four dry-mixed rubberised epoxy asphalt mixtures (DREAMs) are incorporated, with their material parameters (e.g., modulus, density, damping) explicitly defined. Several modelling enhancements are implemented beyond conventional response analysis, including: (i) DREAM-grade-specific Rayleigh damping calibration derived from modal analysis, (ii) a stability-first boundary–mesh prescription. These strategies improve modelling fidelity for non-uniform transition zones. The results show that PEACT dynamic responses remain within acceptable ranges, and that DREAMs provide substantial vibration attenuation, contributing an additional ∼40% reduction on top of the fastener system. From a design perspective, these findings provide practical evidence that graded DREAM layouts can effectively control vertical surface displacement to below 0.5 mm under 350 km/h loading, facilitating smoother stiffness transitions, reduced maintenance demand, and more reliable HSR operation.