While prior work has examined challenges in human-computer interaction research in real-world healthcare settings, less attention has been paid to method development processes. This experience report reflects on our process of developing a method to design an empathetic artificial intelligence (AI) companion with and for emergency department patients. This process unfolded in three phases: In exploration, we developed a card-based interview to investigate empathetic AI behavior. However, realizing that our method and research objective were misaligned, uncertainty emerged as we questioned the implications of advancing a potentially harmful technology. We paused and, in reorientation, carefully adapted our method to ensure responsible research practice. From this experience, we derive four key learnings: distinguishing between (1) designing the right technology and (2) designing technology right while caring for both participants and researchers, (3) acknowledging uncertainty as a research signal, and (4) methodological implications for designing patient-centered empathetic AI.