A combined task-level reinforcement learning and motion planning framework is proposed in this paper to address a multi-class in-rack test tube rearrangement problem. At the task level, the framework uses reinforcement learning to infer a sequence of swap actions while ignoring robotic motion details. At the motion level, the framework accepts the swapping action sequences inferred by task-level agents and plans the detailed robotic pick-and-place motion. The task and motion-level planning form a closed loop with the help of a condition set maintained for each rack slot, which allows the framework to perform replanning and effectively find solutions in the presence of low-level failures. Particularly for reinforcement learning, the framework leverages a distributed deep Q-learning structure with the Dueling Double Deep Q Network (D3QN) to acquire near-optimal policies and uses an A${}^\star$-based post-processing technique to amplify the collected training data. The D3QN and distributed learning help increase training efficiency. The post-processing helps complete unfinished action sequences and remove redundancy, thus making the training data more effective. We carry out both simulations and real-world studies to understand the performance of the proposed framework. The results verify the performance of the RL and post-processing and show that the closed-loop combination improves robustness. The framework is ready to incorporate various sensory feedback. The real-world studies also demonstrated the incorporation.