I know where you're coming from. I don't talk about this a lot, because in retrospect it's really embarrassing, but it was an experience like yours that sent me into my first major period of depression. I don't know your exact circumstances, but I know more or less where you're coming from because I've been there myself. Please keep that in mind as you read my answer.
In my opinion and in my experience, at this point, your only hope is to give up hope. You are not going to date or marry this girl. Consciously, you know that. You have probably known that for a long time. But on a deeper level, you haven't accepted that. You still want to date her. And as long as you let that desire live and work in you, you'll find it hard to move on.
So forget about her. You're about to leave on a mission, so it's the perfect opportunity. Not a single person that you have any contact with will even know that she exists. Don't contact her for two years. No letters, no emails, nothing. Don't talk to your companions about her. Don't write in your journal about her. Thoughts about her will probably come to your mind, but don't dwell on them. Use the same techniques that you would use to avoid inappropriate thoughts, because to you, she IS an inappropriate thought, not because thinking about her is sinful, but because thinking about her hurts you and gives you no benefit. If thinking about her makes you unhappy and does nothing good for you or for anyone else, then the thought is not virtuous, lovely, of good report, or praiseworthy, and it should not be something that you invite into your mind.
One of the wonderful things about being a missionary is that you are so incredibly busy that you don't have time to worry about things that used to distract you. For me, my mission served as an opportunity to wipe my mind of all of my political prejudices via a two-year hiatus from all things political, and left me with a clean slate upon returning home so that I could develop opinions of my own. I think that your mission may serve the same purpose for you and this girl. Let it be a two-year hiatus from thinking about her or anyone else. When you come home, you can come home with a clean slate and a free mind. Will this work for you? I don't know. But I think it's the only really good course of action for you at this point. If you come home in two years and you still haven't moved on, it'll be time to try something different, but for now, do your best to forget about her and give up all hope of ever being with her. I honestly believe it's the best thing that you can do for your happiness and well-being in both the short term and the long term.
Remember, I'm always only an email away.