OP, btw, have you explored liberation theology and its connection to health and medicine? For me this is the most obvious connection and the one that resonates with me the most. Liberation theology is a radical catholic approach to religion that places social justice center stage. It has a long relationship to health and human rights work especially in Latin America.
I haven't read
this but it might be interesting to you. Also,
Paul Farmer's work and the
book about him discuss his connection and attraction to liberation theology. If I'm not mistaken I think Tracy Kidder even asked Dr. Farmer to marry his daughter. I don't know if he had a temporary priesthood or what! If you haven't been exposed to Farmer's work, I highly recommend reading up on him, he is quite an inspiration.