Deep reinforcement learning (DRL) has emerged as a powerful paradigm for solving complex decision-making problems. However, DRL-based systems still face significant dependability challenges particularly in real-time environments due to the simulation-to-reality gap, out-of-distribution observations, and the critical impact of latency. Latency-induced faults, in particular, can lead to unsafe or unstable behaviour, yet existing fault-tolerance approaches to DRL systems lack formal methods to rigorously analyse and optimise performance and safety simultaneously in real-time settings. To address this, we propose a formal framework for designing and analysing real-time switching mechanisms between DRL agents and alternative controllers. Our approach leverages Timed Automata (TAs) for explicit switch logic design, which is then syntactically converted to a Markov Decision Process (MDP) for formal analysis. We develop a novel convex query technique for multi-objective model checking, enabling the optimisation of soft performance objectives while ensuring hard safety constraints for MDPs. Furthermore, we present MOPMC, a GPU-accelerated software tool implementing this technique, demonstrating superior scalability in both model size and objective numbers.