The problem you're referring to is a valid one - that people automatically envision the "normals" (white, male, straight, cisgender) when they think of the stereotypical human being - but "man" and "woman" refer to one's sex and/or gender, and we're talking about sexuality. I know all these areas can intertwine and get quite complex, but I'm uncertain that a new noun like you describe would help the majority of the population break out of that normative thinking, that men and women can't be just that, man or woman, regardless of who they swing for.

I don't know what we should do in terms of linguistics. Your debate brings to mind the "woman" ("man with a womb") quandry. At this point, we may have to start making up entirely new words as we rework our languages - and I do mean plural. First one that pops up for me is "femme" (French, means woman as well as wife, which is an interesting dual definition whereby a woman doesn't exist outside of a married couple from an etymological sense).