Sorry this is kind of late, but still... another similar experience if it helps.
Yo. I'm a post-transition trans female, but lacking the whole gender identity deal. As you said, I always understood how my body should be, but that doesn't really relate to how I understand gender (I don't).
With my folks I decided to just try to keep it straight enough for them to get. I stuck mainly to talking about the issue: i.e. my body. And I kept to the "all kinds of different women people" to explain my weirdness. Eventually I gave a bit more detail about how I see gender, but that was after they'd gotten a lot more used to me. So I went pretty slow.
It also helps that I'm queer, so I think eventually they kind of managed to classify me as "lesbian" and get over how I dress/behave. I did have a rough time early on with a lot of pressure on how to be a proper "woman." And ended up getting into a couple of fights with my folks about that when I insisted on wearing clothes from the guy section of the store. Blah. But it was always super clear for them that I needed to fix my body; the argument was more over what kind of female I'd end up being.
But it worked out pretty well in the end. Heh, my mum bought me a men's necklace for my last birthday. And she says I'm rubbing off on her. She buys men's button ups sometimes now, cause they are super comfy.
I don't really care enough about the pronoun thing to get worked up over it. Honestly, I feel I don't live in a time or place where getting people to call me "they" is a reasonable ask. Maybe in another decade. I figure I'm closer to "she" what with the whole living in society as a girl as far as most people are concerned, so I just go with that.