Register Transfer Level (RTL) design translates high-level specifications into hardware using HDLs such as Verilog. Although LLM-based RTL generation is promising, the scarcity of functionally verifiable high-quality data limits both accuracy and diversity. Existing post-training typically produces a single HDL implementation per specification, lacking awareness of RTL variations needed for different design goals. We propose RTLSeek, a post-training paradigm that applies rule-based Diversity-Oriented Reinforcement Learning to improve RTL correctness and diversity. Our Diversity-Centric Multi-Objective Reward Scheduling integrates expert knowledge with EDA feedback, and a three-stage framework maximizes the utility of limited data. Experiments on the RTLLM benchmark show that RTLSeek surpasses prior methods, with ablation results confirming that encouraging broader design-space exploration improves RTL quality and achieves the principle of "the more generated, the better results." Implementation framework, including the dataset, source code, and model weights, is shown at https://anonymous.4open.science/r/DAC2026ID71-ACB4/.

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