Heh, well, the Dragoons do have helmets covering their faces, don't they? So you wouldn't really be able to tell what gender they are, I suppose.
I'd probably go along with what you'd do, making Refia the female/androgynous and Arc the mage classes. I'd probably make Ingus the heavy warrior classes and Luneth the light warrior and other in-between classes like Red Mage and Geomancer.
Normally I name the characters different names though, on the NES version.