Thank you for your response.
As you say, we are coming at this from different points of origin. Nevertheless, I do think the problems I mentioned are significant.
I think the way the terms "gender" and "gender identity" are used by many today is unfortunate. Not long ago, I was having a disagreement with someone until they realized I was using "gender" to refer to their concept of "gender identity," and vice versa.
There is some objective, fixed, essential reality that lies behind what we call "gender," just as there some objective, fixed, essential reality that lies behind what we call "consciousness." We may not be able to see it clearly, and what we do see is going to be alloyed with things that are not essential to it as it exists in itself; but that's the perception vs. reality problem I mentioned previously. It applies to all things.
It is that objective whatever-it-is that I call "gender." I reserve the term "gender" to refer to this intangible quality because, just as "gender identity," "gender role," "gender expression," etc., are all modifications of the root concept of "gender," this intangible reality is likewise the root of everything else we say about it.
Thus, "gender" is the quality itself, while "gender identity" is my perception of it, i.e. how I identify.
Therefore, while I cannot call gender a construct of any kind, especially social, I can readily accept gender identity as a sort of combination of internal sense and outward perception. This latter sounds like what you're referring to when you say, "[Serrano] discusses our sense of gender [i.e. gender identity] as really being two things - our subconscious sex [i.e. gender, I think] (as separate from our anatomical sex) and our outward gender expression."
Using terms this way, there is no such thing as "gender fluidity," though certainly there can be "gender identity fluidity," "gender expression fluidity," etc.
It is unfortunate that colloquial, non-critical usage of these terms has become established, because they can be difficult to dislodge.