High-density operation in reversed shear configurations is a critical requirement for advanced tokamaks, but it is often limited by the inherent susceptibility to double tearing modes (DTM). This paper systematically investigates the interplay between pellet injection and DTM dynamics through three-dimensional nonlinear magnetohydrodynamic (MHD) simulations, revealing that the time of pellet injection during the evolution of the DTM is the decisive factor influencing discharge stability. We find that pellet injection during the linear growth phase is severely detrimental: the localized cooling caused by ablation induces a sharp increase in the resistivity , triggering an accelerated and more violent DTM crash that culminates in an irreversible thermal quench. To overcome this disruption limit, we propose a novel ‘saturation-stage fueling’ strategy. By synchronizing pellet injection with the nonlinear saturation phase, we demonstrate that the intrinsic radial convective flows driven by magnetic reconnection can be harnessed to transport the injected fuel. This convective mixing effectively homogenizes the deposited density, preventing the formation of localized pressure gradients and resistivity spikes that would otherwise lead to disruptions. Notably, this approach yields dual benefits for plasma performance: it ‘softens’ the mode activity by transforming destructive giant sawteeth into benign, high-frequency, low-amplitude oscillations, and it leverages mode-induced transport to inwardly convect fuel. Simulation results confirm that this method facilitates highly efficient internal fueling, enabling the core density to reach levels significantly above the empirical Greenwald limit while maintaining robust plasma confinement. Ultimately, our findings suggest that instead of striving to entirely avoid instabilities, exploiting the intrinsic convective channels of saturated MHD modes may offer a robust pathway toward achieving high-density, steady-state operation in future fusion devices.