Offline reinforcement learning (offline RL) offers a promising framework for developing control strategies in chemical process systems using historical data, without the risks or costs of online experimentation. This work investigates the application of offline RL to the safe and efficient control of an exothermic polymerisation continuous stirred-tank reactor. We introduce a Gymnasium-compatible simulation environment that captures the reactor's nonlinear dynamics, including reaction kinetics, energy balances, and operational constraints. The environment supports three industrially relevant scenarios: startup, grade change down, and grade change up. It also includes reproducible offline datasets generated from proportional-integral controllers with randomised tunings, providing a benchmark for evaluating offline RL algorithms in realistic process control tasks. We assess behaviour cloning and implicit Q-learning as baseline algorithms, highlighting the challenges offline agents face, including steady-state offsets and degraded performance near setpoints. To address these issues, we propose a novel deployment-time safety layer that performs gradient-based action correction using input convex neural networks (PICNNs) as learned cost models. The PICNN enables real-time, differentiable correction of policy actions by descending a convex, state-conditioned cost surface, without requiring retraining or environment interaction. Experimental results show that offline RL, particularly when combined with convex action correction, can outperform traditional control approaches and maintain stability across all scenarios. These findings demonstrate the feasibility of integrating offline RL with interpretable and safety-aware corrections for high-stakes chemical process control, and lay the groundwork for more reliable data-driven automation in industrial systems.