Decarbonizing downstream steel logistics remains underexplored in sustainable supply chain management. This study proposes a machine learning-enhanced tri-objective optimization framework for the ship stowage planning problem (SSPP). The framework handles heterogeneous finished steel products, including coils, plates, ingots, tubes, and sections. The model simultaneously maximizes deadweight utilization and minimizes a novel Adaptive Weighted Moment Balance (AWMB) index. It also minimizes voyage carbon emissions through a trim-and-heel resistance penalty. A spatial-to-sequential discretization strategy transforms the NP-hard placement problem into a tractable permutation optimization. A deep neural network (DNN) surrogate achieves a 3.57-fold speedup with only 1.52% hypervolume degradation. An improved NSGA-III algorithm with adaptive operators ensures Pareto front exploration. Embedded step-wise moment verification guarantees dynamic stability throughout loading and unloading. Validated on real data from a Chinese steel enterprise, the framework achieves 99.88% deadweight utilization, reduces transverse and longitudinal imbalance by 48.27% and 90.54%, and cuts CO₂ emissions by 95.5% per voyage. SOLAS constraints, load line limits, and CII/FuelEU targets are addressed through embedded stability and capacity constraints. Multi-route and weather-dependent validation remains necessary before fleet-scale deployment.