This paper addresses the critical need for elctrocardiogram (ECG) classifier architectures that balance high classification performance with robust privacy protection against membership inference attacks (MIA). We introduce a comprehensive approach that innovates in both machine learning efficacy and privacy preservation. Key contributions include the development of a privacy estimator to quantify and mitigate privacy leakage in neural network architectures used for ECG classification. Utilizing this privacy estimator, we propose mDARTS (searching ML-based ECG classifier against MIA), integrating MIA's attack loss into the architecture search process to identify architectures that are both accurate and resilient to MIA threats. Our method achieves significant improvements, with an ECG classification accuracy of 92.1% and a lower privacy score of 54.3%, indicating reduced potential for sensitive information leakage. Heuristic experiments refine architecture search parameters specifically for ECG classification, enhancing classifier performance and privacy scores by up to 3.0% and 1.0%, respectively. The framework's adaptability supports user customization, enabling the extraction of architectures that meet specific criteria such as optimal classification performance with minimal privacy risk. By focusing on the intersection of high-performance ECG classification and the mitigation of privacy risks associated with MIA, our study offers a pioneering solution addressing the limitations of previous approaches.