The community of next generation multi-hop satellite networks users will exhibit high variance in geographical distributions. In this regard, efficient traffic control and load balancing schemes are mandatory. Recently the authors have proposed an efficient method for load balancing over multihop satellite networks dubbed an "Explicit Load Balancing" (ELB). In ELB, each satellite monitors its own queue length. If a satellite is about to get congested, it sends an explicit message asking its neighboring satellites to detour a portion of their traffic to alternative paths that do not involve the congesting satellite. Simulation results demonstrated the efficiency of ELB in satellite networks with relatively long inter-satellite link (ISL) delays. In case of satellite constellations with shorter ISL delays, the working of ELB becomes limited as the neighboring satellites are more likely to get promptly congested due to the short detouring range. To cope with this limitation, there is need for explicit exchange of the congestion state among not only neighboring satellites but also satellites at k-hop distance from the congesting satellite. The key idea of the proposed enhancements to ELB consists in the use of the Gaussian distribution to determine the parameter k and the cost of links among satellites that are k-hop distant from the congesting satellite. The performance of the proposed enhancements is evaluated through simulations. The simulation results elucidate that the proposed solution improves the performance of ELB, especially in satellite constellations with short ISL delays.