This study presents a comprehensive analysis of the combustion behavior, performance, and NOx emissions in a diesel-hydrogen dual-fuel high-pressure direct injection (HPDI) compression ignition (CI) heavy-duty engine, utilizing numerical simulations validated against operational-engine experimental data. This study aims to investigate this engine by focusing on two distinct hydrogen rail pressures (295 and 255 bar) and three injection timings (-7, -3, and 1 CAD aTDC), the research explores the dynamics of dual-fuel combustion, particularly the role of injection parameters on engine efficiency and emissions profiles. Validated against six experimental cases, the simulations show the important role of injection timing, with an observed peak efficiency of 54.9% at the highest rail pressure and an SOI of -7 CAD aTDC. As hydrogen injection timing is delayed, a decrease in efficiency and NOx emissions is observed, pointing towards the complex interplay between achieving high combustion efficiency and minimizing environmental impact. This work also establishes a benchmark for the numerical simulation of this novel engine concept, providing a solid foundation for future research and development. This paper contributes valuable insights into optimizing diesel-hydrogen dual-fuel strategies for heavy-duty engines, marking a significant step towards CO2-free mobility solutions.