It makes more sense to sort of factorise each thing into its different components. King is a masculine monarch. Man is a masculine person. Queen and woman are the feminine equivalents.

So king + woman = queen + man is better described as:

Masculine monarch feminine person = feminine monarch masculine person

A bit of reordering of adjectives and it is exactly the same. Even monarch is the wrong word, because you seem to be getting hung up on nouns, when these are all actually a bunch of chained adjectives. Perhaps "regality + nobility + rulery". English is a bad language to describe this, because we tend to noun and verb our adjectives regularly.