Experience-Centred Design (ECD) has been applied in numerous HCI projects to call attention to the particular and dialogical nature of people's experiences with technology. In this paper, we report on ECD within the context of publicly-funded, long-stay residential dementia care, where the approach helped to highlight aspects of participants' felt experience, and informed sensitive and meaningful design responses. This study contributes an extended understanding of the quality of experience and the means of making sense in dementia, as well as unpicking the potential of ECD to support enriched experience and contextual meaning-making for people with dementia. Finally, we delineate what it is about Experience-Centred Design that differentiates the approach from other often-used approaches in designing in dementia contexts: 1) explorative thinking, 2) working within 'cuttings-out of time and space', 3) careful yet expressive methodology and documentation, and 4) working together to imagine futures. We end with considerations of how the contributions of this research may extend to other experience-centred projects in challenging settings.