Premature seal failure induced by the unevenness of interstage pressure distribution in multi-stage brush seals significantly compromises the sealing efficiency of Air-Turbo Rocket (ATR) engines operating under high-pressure (megapascal-level) differential conditions. Conventional pressure equalization designs for such seals often result in significant leakage rate increases. This study addresses the pressure imbalance phenomenon in four-tooth three-stage brush composite seals through a novel fractal–geometric porous-media model, rigorously validated against experimental data. Systematic investigations were conducted to elucidate the effects of structural parameters and operational conditions on both sealing performance and pressure distribution characteristics. Key findings reveal that, under the prototype structure parameter, the first-, second-, and third-stage brush bundles account for 18.3%, 30.0%, and 43.3% of the total pressure drop, respectively, with grate teeth contributing 8.4%, demonstrating an inherent pressure imbalance. Axial brush spacing exhibits a minimal impact on the pressure distribution, while the gradient thickness settings of the brush bundles show limited influence. Radial clearance optimization and gradient backplate height adjustment effectively regulate pressure distribution, albeit with associated leakage rate increases. Structural modifications based on these principles achieved only a 5.8% leakage increment while reducing the maximum bundle pressure drop by 23%, demonstrating effective pressure balancing. A simplified analysis of entropy reveals that the fundamental mechanism governing the pressure imbalance stems from non-uniform entropy generation caused by aerodynamic damping dissipation across sequential brush stages. These findings establish a dampened dissipation-based theoretical framework for designing high-performance multistage brush seals in aerospace applications, providing critical insights for achieving an optimal balance between leakage control and pressure equalization in extreme-pressure environments.