I'd also like to offer whatever I can to the table advice-wise.
What you've done here is come out about your identity to total strangers. We don't even know who you are; until finding your thread, I would have no clue that you even exist. Your family, by contrast, has been there your entire life; there shouldn't be anyone out there with a closer relationship than family. So I can say with some degree of confidence, they'd accept things. Your sisters and aunt are already accepting of who you are, though despite your concerns about your father's stance, I'd say the one who would have the hardest time coming around to this is your mother. Christians are so xenophobic sometimes, for my inability to think of a better term =.=
If you'd like to take on her fears or concerns, I think the best thing you can tell a born-again Christian is that this was how God - who apparently knows and controls everything - willed you to be, and that even if she has some issues with your identity, everyone gets those with people. It'd just be the simplest way to explain a complex thing like gender identity issues. "This is how God made you" and "What would Jesus do?", in addition to the fact that you're her child, should help her understand the right thing to do. If she does disown you...well, that's not very Christian-like, tolerant, or motherly at all; a stark contrast to what you've said about her.
Sadly, I can't offer much on how to put this to your father. The best I can offer is to bring things in from a psychological point of view. Transphobic doctors are exactly that: transphobic. However, anything ending in "-phobic" typically means it's an irrational fear or dislike of something, "irrational" being the keyword here. There's nothing wrong with a boy thinking they should be a girl, or vice versa. On the patient's side of things, the human mind is - despite how much research we've put into it - a complete and total mystery. Whoever said space is the final frontier obviously never saw the inner workings of his brain.
And please don't think I'm telling you to take advantage of your mother's religion to persuade her; not at all. Christianity is supposed to be a religion that accepts all walks of life, though it seems somewhere down the line, a fair few of them forgot just what they wanted in the first place. Likewise, I'm not saying to take advantage of linguistic and psychological facts to persuade your father; just to open his eyes to that there's no right or wrong in this issue except the ones we ourselves put out there. That's all I've got for you though. I wish I could offer more advice, but these kinds of situations aren't quite in my list of things I've got ready advice for ^_^;