Predicting public transit incident duration from unstructured text alerts is a critical but challenging task. Addressing the domain sparsity of transit operations with standard Supervised Fine-Tuning (SFT) is difficult, as the task involves noisy, continuous labels and lacks reliable expert demonstrations for reasoning. While Reinforcement Learning from Verifiable Rewards (RLVR) excels at tasks with binary correctness, like mathematics, its applicability to noisy, continuous forecasting is an open question. This work, to our knowledge, is the first to bridge the gap between RLVR LLM training with the critical, real-world forecasting challenges in public transit operations. We adapt RLVR to this task by introducing a tolerance-based, shaped reward function that grants partial credit within a continuous error margin, rather than demanding a single correct answer. We systematically evaluate this framework on a curated dataset of NYC MTA service alerts. Our findings show that general-purpose, instruction-tuned LLMs significantly outperform specialized math-reasoning models, which struggle with the ambiguous, real-world text. We empirically demonstrate that the binary reward is unstable and degrades performance, whereas our shaped reward design is critical and allows our model to dominate on the most challenging metrics. While classical regressors are superior at minimizing overall MAE or MSE, our RLVR approach achieved a 35\% relative improvement in 5-minute accuracy (Acc@5) over the strongest baseline. This demonstrates that RLVR can be successfully adapted to real-world, noisy forecasting, but requires a verifier design that reflects the continuous nature of the problem.