Sorry if it's inappropriate for me to reply to this, as I'm straight, but I wanted to give you some feedback, as you've not really had any yet, unfortunately.

So, as I've said, I'm straight. But, I don't see anything wrong with your thinking. However, you've associated the word "lesbian" with something that "lesbian" solely isn't. Lesbian merely means a female who is exclusively "interested" in other females, right? If you were into both, it'd be "bisexual", is that right? I'm no master at orientation.

My point is, you're a lesbian, and that's fine! Ditch that association; it's not fair on you. Embrace who you are. You can stress over semantics, or you can accept that you are a lesbian, just perhaps not a stereotypical one, and that's fine!

I'm sure "homosexuals" (seems almost derogatory or sarcastic to say that, nowadays) feel a similar way, especially those who are not the typical gay men, all "camp" 'n' what-not.

Hope these words, coming from a straight man, can still mean something to you.

However, if referring to yourself as "gay woman" makes you feel more comfortable, then fair enough, but ... semantics.