Without the need for a clean reference, non-intrusive speech assessment methods have caught great attention for objective evaluations. While deep learning models have been used to develop non-intrusive speech assessment methods with promising results, there is limited research on hearing-impaired subjects. This study proposes a multi-objective non-intrusive hearing-aid speech assessment model, called HASA-Net Large, which predicts speech quality and intelligibility scores based on input speech signals and specified hearing-loss patterns. Our experiments showed the utilization of pre-trained SSL models leads to a significant boost in speech quality and intelligibility predictions compared to using spectrograms as input. Additionally, we examined three distinct fine-tuning approaches that resulted in further performance improvements. Furthermore, we demonstrated that incorporating SSL models resulted in greater transferability to OOD dataset. Finally, this study introduces HASA-Net Large, which is a non-invasive approach for evaluating speech quality and intelligibility. HASA-Net Large utilizes raw waveforms and hearing-loss patterns to accurately predict speech quality and intelligibility levels for individuals with normal and impaired hearing and demonstrates superior prediction performance and transferability.