Despite advances in multimodal cancer prognosis, robust performance in practical settings remains hindered by three critical barriers: ubiquitous data incompleteness, failure to model cancer-specific biology, and cross-institutional instability. We address these practical challenges through a cancer-type-aware framework that uniquely combines adaptive gated fusion for missing modalities, hybrid architecture for cancer heterogeneity, and demonstrated cross-institutional robustness. By establishing histopathology as the universally available anchor modality while adaptively incorporating RNA expression and clinical text through gated fusion, our framework maintains robust performance under realistic data constraints. Evaluation across 10 The Cancer Genome Atlas cancer types demonstrated superior performance (C-indices 0.578-0.778; mean 0.670 $\pm $ 0.066), with state-of-the-art results in six cancer types. The framework maintained predictive performance under missing data scenarios, with C-indices ranging from 0.621 to 0.627 for missing RNA and from 0.568 to 0.606 for missing clinical text. Cross-institutional validation across 12-38 centers demonstrated robust cross-institutional performance (standard deviations <0.040 in eight of 10 cancer types). This methodological framework addresses key technical prerequisites-handling missing data, modeling cancer heterogeneity, and ensuring cross-institutional stability-for multimodal survival prediction, providing computational foundations necessary for future prospective clinical validation.