Multimodal MRI is essential for brain tumor segmentation, yet missing modalities in clinical practice cause existing methods to exhibit >40% performance variance across modality combinations, rendering them clinically unreliable. We propose AMGFormer, achieving significantly improved stability through three synergistic modules: (1) QuadIntegrator Bridge (QIB) enabling spatially adaptive fusion maintaining consistent predictions regardless of available modalities, (2) Multi-Granular Attention Orchestrator (MGAO) focusing on pathological regions to reduce background sensitivity, and (3) Modality Quality-Aware Enhancement (MQAE) preventing error propagation from corrupted sequences. On BraTS 2018, our method achieves 89.33% WT, 82.70% TC, 67.23% ET Dice scores with <0.5% variance across 15 modality combinations, solving the stability crisis. Single-modality ET segmentation shows 40-81% relative improvements over state-of-the-art methods. The method generalizes to BraTS 2020/2021, achieving up to 92.44% WT, 89.91% TC, 84.57% ET. The model demonstrates potential for clinical deployment with 1.2s inference. Code: https://github.com/guochengxiangives/AMGFormer.