Abstract: To address the complex challenges posed by node heterogeneity and connectivity changes in integrated space-air-ground heterogeneous networks, this paper proposes a transmission control method with bounded, loop-free, and blocking-free policy update capabilities. This method incorporates network routing algorithms into the transmission control framework through cross-layer cooperative control. The selection of routing update nodes is modeled as a node search problem, ensuring that the resources involved in network transmission are bounded. On this basis, a breadth-first heuristic incremental search algorithm is designed to efficiently update both global and local routing configurations, ensuring that new paths are loop-free and devoid of network black holes. Additionally, to adapt to the volatility of integrated space-air-ground heterogeneous networks, a multi-mode hybrid congestion control mechanism is designed. This mechanism can switch to a more gradual window-increase mode when approaching the network bandwidth threshold, promptly adjusting policies to handle various potential network conditions. Simulation results demonstrate that the HWCTC method provides high-quality data transmission services in dynamic and high packet loss rate integrated space-air-ground heterogeneous network environments. Compared to the classical Cubic and Reno algorithms, HWCTC achieves approximately 61.5% improvement in throughput, significantly enhancing data transmission stability and effectively reducing the impact of dynamic node routing changes on transmission performance.