As human-agent medical collaboration evolves with the rapid advancement of AI systems, careful trust considerations are needed to overcome barriers to adoption and usability. Although human-automation interaction and interface design have been widely studied from the perspective of human→agent trust, effective medical collaboration requires mutual trust. Transdisciplinary efforts are needed to design medical systems and user interfaces (UIs) that consider human↔agent trust as a fundamental part of the interaction. The design of medical systems for astronaut-agent teaming on long-duration human spaceflight (LDHSF) represents a well-defined and focused edge case that allows for specifying key aspects for mutual justifiable trust-informed interaction design and offers opportunities for broader applications. While astronaut-agent collaboration and the integration of emerging technologies could enable crew independence from ground medical support, effective teaming requires the agent to be aware when the human is unable to perform a task or requires assistance adaptation. Applying a human-centered design approach, we conducted qualitative interviews, stakeholder meetings, and design workshop sessions. The Subject Matter Experts (SMEs) represented diverse fields, including astronauts, space medicine, human factors, computing, human-computer interaction, engineering, and space systems. In this paper, we discuss key insights related to trust challenges and opportunities of astronaut-agent medical interfaces, presenting selected outputs from co-design sessions related to medical interaction during LDHSF. We illustrate practical examples from a case study development of a trust-driven, trust-adaptive Exploration Medical Ecosystem Design Interface (ExMEDI), and highlight opportunities for future work.