Automated speaking assessment (ASA) typically involves automatic speech recognition (ASR) and hand-crafted feature extraction from the ASR transcript of a learner's speech. Recently, self-supervised learning (SSL) has shown stellar performance compared to traditional methods. However, SSL-based ASA systems are faced with at least three data-related challenges: limited annotated data, uneven distribution of learner proficiency levels and non-uniform score intervals between different CEFR proficiency levels. To address these challenges, we explore the use of two novel modeling strategies: metric-based classification and loss reweighting, leveraging distinct SSL-based embedding features. Extensive experimental results on the ICNALE benchmark dataset suggest that our approach can outperform existing strong baselines by a sizable margin, achieving a significant improvement of more than 10% in CEFR prediction accuracy.