Your devotion to the Navy is most admirable. They would be doing themselves a great disservice by getting rid of you. Let me parry and riposte by pointing out that while it may be dishonest to lie about having a mental disorder, A) it seems that so far no one has asked and B) how is it any less dishonest than getting rid of DADT, having an LGBT pride month, and still kicking out anyone who falls under the "T"? And which is the greater evil? GID has nothing to do with your judgement in an emergency or during normal ops, unlike being drunk or high. Your reaction speed is not lowered, your ability to calmly act and contain a problem is not diminished by your predilection to wearing women's clothing, so the fact that GID is considered a mental disorder is irrelevant. In the parlance of the non-nuclear navy, "you're nuking it." Sorry, I had to say it at least onceIt's an issue of morality and appearances, and that's all it's ever been.
Again, you should get a NAM for your selflessness and devotion. That line of thinking applies to things like a heroin addiction or being approached by a foreign agent (which does happen, believe me). No reasonable person is going to require you to turn yourself in if you are in violation of any tiny rule. What do you think of a person who goes to sick bay every time their big toe hurts? S***bag malingerer, right? So why should you have to turn yourself in for something that doesn't affect your job performance?
You should be PISSED. Royally. I know I am. The injustice of it makes me sick. Especially when you consider that the military overlooked the fact that they are now berthing people who are sexually attracted to each other in the same berthing area (which is unfair for everybody, especially the gays. It would be like sticking me in the female berthing and saying "don't touch. Don't even look.") But apparently the clothes we choose to wear are problematic. It is truly unfair. But it's not as bad as perhaps you're led to believe. I live in barracks and I still dress almost every day. Going out is tricky, but it's incentive to take care of myself and pass as well as I can. No one here can tell you what to do, but Michelle makes an excellent point in that if you choose to turn yourself in or not deny it if someone makes a fuss, then it's a quick, quiet medical discharge. No big deal, and it won't stop you from gaining employment in the outside. If you choose to stay in, just keep it quiet. I've been asked before. I jokingly said "I'm under no obligation to answer you, chief" and that's all that ever came of that. A lot of people don't know that it's still a disqualifier. I know a lot of people who think that DADT going away means that any LGBT-whatever is just fine.
Oh, one more thing: coasting under the radar is not hypocrisy. I know it seems like it, but it's not. Consider, 200 years ago, war was conducted by rank after rank of riflemen who stood across the field from the enemy, very open, no attempt to find cover and volley back and forth. The idea of using cover and ambush tactics on the battlefield would have been considered the height of cowardice. Nowadays doing things their way seems like suicide. Likewise, you can't beat the system by standing up to it. You have to take the modern approach. Live to fight another day.