So it's basically how you perceive yourself?

I am aware I am female the same way female people who identify as men are aware they are female. All female transitioners who identify as men perceive themselves as female as taking testosterone to imitate appearance of the male sex requires having a female perception, had they been unaware of their own femaleness they wouldn’t been able to be dysphoric about their female sex and thus wouldn’t be trans to begin with.

I see myself as female, and would see myself as female regardless of my birth sex.

Then you don’t mean you see yourself as female when you say you see yourself as female as you you don’t refer to female but a gender identity. If female and male are gender identities then according your definition above a gender identity is the personal conception of oneself of having a gender identity, another gender identity, both or neither. That’s a circular definition.

If I was born male, I would transition via hormones and surgery, because being male would cause me dysphoria.

When I have asked people it seems be like fifty fifty, half not caring if they had been born the opposite sex and half who would rather not (but those who said they would rather not said they still wouldn't transition but as transition can't make someone the opposite sex, so they would rather just come to term with it). So if gender identity is body preferences then it would make it morally wrong to call someone a gender identity unless you have proof the person indeed has the body preference your refer to, as otherwise you risk lying about something very personal about them. So if female to you is the preference to have a female body it would be immoral of you to call someone female before asking and making sure this person indeed prefers a female body, and if this person is indifferent it would be immoral to call that person female, as indifference and preference are different things that ought to be distinguished.