She knows you want to bang her so lets just cut the bullsh!t right now. I'm not going to beat you down over this, but one thing teenage, young men need to foster in themselves is a brutal self-honesty, so lets start now OK? Your mistake is in thinking that desexualizing yourself will in some way make you unique and "not-like-other-guys". The idea being that a girl - and particularly an equally inexperienced teenage girl - will have the depth of maturity to appreciate this hold you in higher interest than other guys. Sorry, but she can't and she wont. It's exactly that sexualized nature that she fears (thanks to her religious upbringing) and is excited by. In desexualizing yourself you've cut one leg off and you're trying to sprint.
It's OK to be sexual. You only self-defeat when you neuter yourself voluntarily. Even in the most proper, orthodox of religious marriages the couple had to be hot enough to want to ƒuck each other at SOME point in their being single in order to get married in the first place. That means desire, that means the idea of sex with that person made the other one hot.
Now then, lets clear this up, men and women cannot be friends, or at least not in the way that most people perceive same sex friendship to be. Now the natural resoponse to this from a well conditioned AFC is "I have lots of female friends" or "what are you trying to say, I can't have female friends, they all haffta be enemies?" Which of course is the standard binary (black or white, all or nothing) retort from a trained AFC thinking anyone suggesting that men and women's relations as friends could be anything less than equitable and fulfilling is just neanderthal chauvinist thinking thawed out from cryogenic freeze in the 1950s. But you are incorrect - not because you wouldn't genuinely want to be a woman's friend, but because she cannot be yours. There are fundamental differences in the ways men and women view friendship within their own sex and the ways this transfers to the concept of intergender friendship.
Quite simply there are limitations on the degree to which a friendship can develop between men and women. The easy illustration of this is that at some point your female "friend" will become intimately involved with another male; at which point the quality of what you perceived as a legitimate friendship will decay. It must decay for her new, intimate relationship to mature. For instance, I've been married for 12 years now; were I to entertain a deep freindship with another female (particualrly an attractive female) other than my wife, my interest in this woman automatically becomes suspect of infidelity - and of course the same holds true for women with men-friends.
It's not to say that you cannot have female aquaintances, or that you must necessarily be rude or ignore all women with misogynistic contempt; that is binary thinking once again, but it is to say that the degree of friendship that you can experience with women (as a man) in comparison to same sex friendships will always be limited due to sexual differences. Most men will only ever engage in friendships with women that they find attractive and/or interesting which of course is colored by their attraction to that woman (as in your case).
Now I'm sure you'll play the "not in my case" card and attempt to tell me how much an exception to the rule you are, to which I'll say, even if you legitimately are, it makes no difference. Because the very nature of an intergender friendship is ALWAYS going to be limited by sexual differences.
Even the best, most asexual, platonic, male-female friendships will be subject to mitigation based on sex. So get out of your head now that there even is a so called "friend zone" with any woman. You're either intimate with her or you're not. Women have boyfriends and girlfriends, if you're not ƒucking her, you're her girlfriend, simple as that. There is no friend zone - there is only the limbo between you being fooled that a girl is actually a friend on an equitable level to your same sex friends, and you understanding that as soon as she becomes intimate with another guy your attentions will become a liability to any relationship she might want to have with the new sexual interest and she puts you off, or you do the same when you become so involved with another girl.