Airborne Gamma-Ray Spectrometry (AGRS) is a critical tool for radiological emergency response, enabling the rapid identification and quantification of hazardous terrestrial radionuclides over large areas. However, existing calibration methods are limited to only a few gamma-ray sources, excluding most radionuclides released in severe nuclear accidents and nuclear weapon detonations, which compromises effective response and accurate risk assessments in such incidents. Here, we present a high-fidelity Monte Carlo model that overcomes these limitations, offering full-spectrum calibration for any gamma-ray source. Unlike previous approaches, our model integrates a detailed mass model of the aircraft and a calibrated non-proportional scintillation model, enabling accurate event-by-event predictions of the spectrometer's response to arbitrarily complex gamma-ray fields. Validation measurements in near-, mid-, and far-field scenarios demonstrate that the developed model not only effectively addresses the large deficiencies of previous approaches, but also achieves the accuracy and precision required to supersede traditional empirical calibration methods. These results mark a major advancement in AGRS. The developed calibration methodology not only allows for the generation of high-fidelity spectral signatures for any gamma-ray source, but also reduces calibration time and costs, minimizes reliance on high-intensity calibration sources, and eliminates the generation of related radioactive waste. The approach presented here serves as a critical step toward integrating advanced full-spectrum data reduction methods for AGRS, which could unlock promising new capabilities for these systems beyond emergency response, including the quantification of the cosmic-ray flux in the atmosphere for geophysical research and the identification of trace-level airborne radionuclides in nuclear security applications.