Astrologian was originally chemist, reskinned to fit an ishgard theme.
just think of the card skills as mixing ingredients and the skillset becomes pretty easy to imagine.

classes that could be made to work as a healer currently would be sage, shaman, oracle, mediator, dancer(but not really the way people think, the game is too reliant on bursty healing), and red mage(but i see this fitting the role of bard/machinist more as a caster/support)