Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient. This deficiency, coupled with array imperfections, degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, an adaptive diagonal loading method is developed that guarantees the WNG remains strictly within specified bounds. By leveraging the Kantorovich inequality, the desired WNG is mapped to a strict upper bound on the condition number of the correlation matrix. Furthermore, the method results in three estimation techniques for the adaptive loading level, ranging from trace-based bounding to exact eigenvalue decomposition, offering scalable computational complexities of $\mathcal{O}(M)$, $\mathcal{O}(M^2)$, and $\mathcal{O}(M^3)$. The adaptive diagonal approach approach demonstrates highly stable beamforming under fast-changing environment states.