Accurate predictions of particle creation from accelerating mirrors are essential for interpreting forthcoming analog Hawking radiation experiments, yet the associated Bogoliubov integrals are generally analytically intractable for realistic trajectories. We introduce the Inertial Replacement Method (IRM), a hybrid analytic–numerical framework that reduces the infinite-domain Bogoliubov integral to a finite-domain problem by replacing the asymptotic tails of the trajectory with inertial extensions. This allows numerical evaluation to be restricted to the finite accelerating region, with controlled boundary contributions from the asymptotic segments. We derive perturbative bounds on the IRM-induced deviations, providing accuracy estimates and guidance for segmentation. The method is validated against trajectories with known analytic solutions and applied to a fully numerical Chen–Mourou plasma-mirror trajectory obtained from particle-in-cell (PIC) simulations relevant to the planned AnaBHEL experiment. Our results demonstrate that, within the IRM framework, the characteristic ray-tracing mapping in the finite accelerating region suffices to capture the overall shape of the particle number spectrum, while the result is insensitive to the further inclusion of the asymptotic tails. This suggests a more local perspective of the particle creation from the moving mirrors associated with its accelerating motion, rather than as a consequence of the detailed global structure of the spacetime. Also, these results establish the IRM as a reliable and applicable computational framework for particle creation in realistic analog-gravity systems.