Machine unlearning (MUL) focuses on removing the influence of specific subsets of data (such as noisy, poisoned, or privacy-sensitive data) from pretrained models. MUL methods typically rely on specialized forms of fine-tuning. Recent research has shown that data memorization is a key characteristic defining the difficulty of MUL. As a result, novel memorization-based unlearning methods have been developed, demonstrating exceptional performance with respect to unlearning quality, while maintaining high performance for model utility. Alas, these methods depend on knowing the memorization scores of data points and computing said scores is a notoriously time-consuming process. This in turn severely limits the scalability of these solutions and their practical impact for real-world applications. In this work, we tackle these scalability challenges of state-of-the-art memorization-based MUL algorithms using a series of memorization-score proxies. We first analyze the profiles of various proxies and then evaluate the performance of state-of-the-art (memorization-based) MUL algorithms in terms of both accuracy and privacy preservation. Our empirical results show that these proxies can introduce accuracy on par with full memorization-based unlearning while dramatically improving scalability. We view this work as an important step toward scalable and efficient machine unlearning.