The detection of quantum gravity signatures in astrophysical observations faces fundamental challenges due to the extremely small magnitude of expected effects and the computational complexity required for precision modelling. We present a comprehensive computational framework that addresses these challenges through advanced numerical methods specifically designed for quantum gravity phenomenology. Our numerical implementation incorporates modified stellar structure calculations, advanced parameter estimation algorithms, and high-performance computing techniques to achieve the precision required for detecting subtle quantum gravity signatures in astronomical observations. The framework includes robust validation protocols, extensive benchmarking against analytical limits, and comprehensive uncertainty quantification methods that ensure reliable scientific conclusions. Through systematic convergence studies and comparison with existing literature, we demonstrate numerical accuracy at the level of for stellar structure calculations and for parameter estimation, sufficient for current and next-generation observational precision. Our computational infrastructure scales efficiently to problems involving millions of parameters and enables exploration of the full multidimensional parameter spaces relevant to quantum gravity phenomenology. Looking toward the future, we provide detailed projections for the observational capabilities of next-generation facilities, including ATHENA, Lynx, Einstein Telescope, and Cosmic Explorer, demonstrating that definitive tests of quantum gravity theories should be achievable within two decades. The computational methods and software tools developed in this work are made publicly available to enable community-wide exploitation of multi-messenger observations for fundamental physics research. These developments establish the computational foundation necessary for the transition from preliminary constraints to precision tests of quantum gravity theories through astrophysical observations.