In the second stage of ultra-high-pressure ethylene compressors, operation pressures can reach up to 250 MPa, often resulting in wear failure of the plunger–packing friction pair. The conventional mixed elastohydrodynamic lubrication (EHL) model is inadequate for accurately modeling the behavior of metallic sealing packings with rough surfaces. This study proposes an improved method by integrating the Greenwood–Tripp (GT) contact model with traditional mixed EHL theory. The results demonstrate strong concordance with existing research, showcasing the efficacy of the proposed approach. Furthermore, the lubrication behavior of metal rectangular sealing elements under complex and highly variable operating conditions is examined. Contrary to traditional EHL predictions, results indicate that an increase in plunger velocity does not enhance the fluid load-carrying capacity; instead, it expands the cavitation zone within the contact region. Notably, the peak asperity pressure is observed during the latter part of the instroke, where the load is maximized and the velocity remains comparatively high, rather than at the termination of the compression stroke, characterized by high pressure and low velocity. Additionally, elevated operating temperatures are shown to increase the friction coefficient while concurrently reducing the leakage rate, potentially creating a positive feedback loop that raises interface temperature and accelerates wear during practical operations. The proposed model is validated through experiments conducted with actual materials from the plunger–packing configuration in hyper compressors, and experimental measurements of friction coefficients corroborate numerical simulations based on the tested sample contact model.