Cardiac cell network segmentation is uniquely challenging because cardiomyocytes, unlike other cell types, form morphologically complex multicellular structures, causing generalist models like Cellpose to oversegment and perform inaccurately. We use our unique live cell imaging dataset of self-organised HL-1 networks to propose and assess various algorithmic configurations based on combinations of the Cellpose model and the Segment Anything Model, equipped with multiple pre- and post-processing routines. Our results demonstrate the advantages of integrating equalisation-based pre-processing with median filtering, fine-tuning Cellpose, and incorporating our post-processing routine into the segmentation pipeline, achieving up to 85% accuracy, 96% recall, 91% DICE, and 88% precision, while mitigating oversegmentation.