Purpose: In sleep medicine, assessing the evolution of a subject's sleep often involves the costly manual scoring of electroencephalographic (EEG) signals. In recent years, a number of Deep Learning approaches have been proposed to automate this process, mainly by extracting features from said signals. However, despite some promising developments in related problems, such as Brain-Computer Interfaces, analyses of the covariances between brain regions remain underutilized in sleep stage scoring. Methods: Expanding upon our previous work, we investigate the capabilities of SPDTransNet, a Transformer-derived network designed to classify sleep stages from EEG data through timeseries of covariance matrices. Furthermore, we present a novel way of integrating learned signal-wise features into said matrices without sacrificing their Symmetric Definite Positive (SPD) nature. Results: Through comparison with other State-of-the-Art models within a methodology optimized for class-wise performance, we achieve a level of performance at or beyond various State-of-the-Art models, both in single-dataset and - particularly - multi-dataset experiments. Conclusion: In this article, we prove the capabilities of our SPDTransNet model, particularly its adaptability to multi-dataset tasks, within the context of EEG sleep stage scoring - though it could easily be adapted to any classification task involving timeseries of covariance matrices.