Interesting, very interesting, indeed...
It is so very fascinating how within the gender-variant community, there exists, side-by-side, those that despise their particular birth status and those that would gladly exchange their own to possess that which is despised by another.
I was born xx intersex, and have been diagnosed as hermaphroditic, and nothing would make me happier than to have been born neither, but just a normal baby girl. That which I am seeking to 'correct', is very much that which you are seeking to embrace, if I read you rightly. Is it no wonder there are sometimes moments of friction within our community? ;-)
It was very conceivable that I could have had my vagina re-opened, without losing my very enlarged clitoris. Dr. Reed, in Miami, suggested he could make that a reality for me, if I had so desired. It is also true that had my parents not sought to 'normalize' me as a 'male', I would have lived my life as a fertile woman, but with a clitoris capable of penetrating and giving pleasure.
Ironic, no?
But, all that aside, there remains your question as to how to self-identify going forward with your journey...
Yes, intersex is usually reserved for those born with tissues that are perceived as male and female, concurrently. I am loathe to be identified as such, for whatever reason, and identify solely by my gender identity, which is female.
And, yes, the term hermaphrodite is usually reserved for those born that way, and it overlaps with intersex, but the additional downside is that it can also be seen as pejorative. I know I recoil from being described as a hermaphrodite, but hey, that's me.
I am trying to wrap my head around your question, and help you find a useful answer. There certainly must be a way to describe yourself and your journey that will satisfy both your need to define yourself, and to make who you are plain to others when you share your self-description.
I'll get back to you when I have something, hopefully somebody else will have an epiphany soon, instead, lol.
Tough question, oh my!
Good luck!!
Missy