Major Depressive Disorder (MDD) is a common worldwide mental health issue with high associated socioeconomic costs. The prediction and automatic detection of MDD can, therefore, make a huge impact on society. Speech, as a non-invasive, easy to collect signal, is a promising marker to aid the diagnosis and assessment of MDD. In this regard, speech samples were collected as part of the Remote Assessment of Disease and Relapse in Major Depressive Disorder (RADAR-MDD) research programme. RADAR-MDD was an observational cohort study in which speech and other digital biomarkers were collected from a cohort of individuals with a history of MDD in Spain, United Kingdom and the Netherlands. In this paper, the RADAR-MDD speech corpus was taken as an experimental framework to test the efficacy of a Sequence-to-Sequence model with a local attention mechanism in a two-class depression severity classification paradigm. Additionally, a novel training method, HARD-Training, is proposed. It is a methodology based on the selection of more ambiguous samples for the model training, and inspired by the curriculum learning paradigm. HARD-Training was found to consistently improve - with an average increment of 8.6% - the performance of our classifiers for both of two speech elicitation tasks used and each collection site of the RADAR-MDD speech corpus. With this novel methodology, our Sequence-to-Sequence model was able to effectively detect MDD severity regardless of language. Finally, recognising the need for greater awareness of potential algorithmic bias, we conduct an additional analysis of our results separately for each gender.