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Online 3D bin packing with a processing buffer requires choosing which box to pack, its orientation, and its placement while keeping the stack stable under unknown future arrivals. A collapse ends the episode and forfeits the remaining volume. Existing methods use geometric rules or hard stability masks, limiting how risk can influence the joint choice of box, orientation, and placement. We propose Stability-Hybrid On-Policy Reinforcement Learning (SHORE), which combines a learned stability probability of a placement with an on-policy estimate of its return conditional on stability. A 3D U-Net learns stability from executed outcomes and simulated alternatives, revealing outcomes of actions underrepresented in early rollouts. A discrete on-policy actor--critic uses stability predictions in both its action values and policy prior, with gates that limit the effect of an untrained or changing model. In deployment, SHORE does not require additional search or simulation overhead. In Isaac Gym, SHORE reaches 73\% space utilization by 0.4M environment steps, while the same learner without stability modeling reaches that level at about 1M. On the expanded 60-box set, SHORE achieves 0.734 space utilization versus 0.588 for the GOPT state-of-the-art baseline, with a higher placement-failure frequency (1.03\% vs. 0.63\%), trading more risk for greater packed volume. The results show faster learning and higher utilization on the more demanding realistic box arrival set. Ablations suggest that simulated alternatives provide useful early supervision, while executed outcomes alone sustain later performance. We also demonstrate the method on a real robot to verify the simplicity of integrating the method to real bin packing pipelines.