Fine-tuning transformer-based models for part-of-speech tagging of unedited Greek text has outperformed traditional systems. However, when applied to lemmatisation or morphological analysis, fine-tuning has not yet achieved competitive results. This paper explores various approaches to combine morphological features to both reduce label complexity and enhance multi-task training. Specifically, we group three nominal features into a single label, and combine the three most distinctive features of verbs into another unified label. These combined labels are used to fine-tune DBBERT, a BERT model pre-trained on both ancient and modern Greek. Additionally, we experiment with joint training -- both among these labels and in combination with POS tagging -- within a multi-task framework to improve performance by transferring parameters. To evaluate our models, we use a manually annotated gold standard from the Database of Byzantine Book Epigrams. Our results show a nearly 9 pp. improvement, demonstrating that multi-task learning is a promising approach for linguistic annotation in less standardised corpora.