Survival analysis is complicated by censored data, high-dimensional features, and non-linear interactions. Classical models offer interpretability and superior calibration but are restricted to linear or predefined functional forms, while deep learning models are flexible and achieve strong discriminative performance, but tend to produce poorly calibrated survival estimates. To address this trade-off, we propose GRAFT (Gated Residual Accelerated Failure Time), a novel AFT model that decouples prognostic ranking from survival calibration. GRAFT's hybrid architecture combines a linear AFT model with a non-linear residual neural network, and it also integrates stochastic gates for automatic feature selection. The model is trained by optimizing a differentiable, C-index-aligned ranking loss using stochastic conditional imputation from local Kaplan-Meier estimators, while calibrated survival estimates are obtained through simple post-training calibration. In public benchmarks, GRAFT outperforms baselines in discrimination and calibration, while remaining robust and sparse in high-noise settings.