The global rise in aging populations is intensifying the demand for intelligent assistive technologies in long-term care settings. However, many existing solutions fail to reflect the complex, emotional, and practical realities of caregiving, leading to limited adoption and trust. This study introduces an experience-driven participatory design framework that translates the tacit knowledge of frontline caregivers into actionable design criteria for intelligent nursing products. Through field observations, participatory interviews, and narrative analysis conducted in a hospital setting, we uncovered key friction points and informal caregiving strategies. These insights were transformed into design opportunities using scenario mapping and low-fidelity prototyping. A video-based usability evaluation with five participants demonstrated early acceptance of a robotic arm prototype for basic care tasks, with positive feedback on functionality, emotional comfort, and perceived safety. Our findings support the use of experience-centered design as a strategy for developing emotionally resonant and context-aware healthcare technologies. The proposed four-phase framework offers a transferable methodology for HCI researchers and healthcare innovation teams aiming to build inclusive, human-centered care systems.