I want to say this in a gentle and supportive way, so please take this as advice that will help you.
Okay, everything you have just described has wreaked of AFC and beta male. The good thing is, you seem aware of this.
Now, I will tell you what I would do. Hashby, I NEVER. I mean NEVER EVER allow a girl I want to fcloze put me into the friends category. My first instinct would be to just completely forget this girl and focus your energy on the other billions of women on this earth. Don't be a beta male and don't let her "friend" you. It's better to not be a friend at all than to submit yourself to that position for her.
If you want to give it another shot you have to put her in an uncomfortable position so that she either submits to you or she says fuck it and doesn't contact you anymore because she can't get what she wants (making you a pussy and puting you in the friends zone). What is that thing you have to do that makes her uncomfortable? You have to imply that the next time you meet it will be of a romantic/sexual nature.
Here's the email you're going to send back to her:
[Hey, it's good to hear from you. Funny, but when I saw your name on my message list it took me a while to remember who you were. So how's your summer been going so far? It's been going awesome for me. I met this exchange student from Finland. Dude, I had no idea people from Finland are so nice. This girl takes me out a lot when I have time. I've been working out at the gym too. There's a group of girls there too that have been inviting me out from time to time. Now that I think of it, there's one girl in that group that kind of reminds me of you. She's sooooo annoying. Ughhhh!!! She always runs up behind me and jumps on my back for a piggy back ride and then I have to tickle her to get her off. What the hell is that all about??
Umm, sorry, I only let people of a certain ilk be my friends. You haven't made the cut yet

But we could start out with a date. How about we go to that lookout point and chill out and talk. Before you get too excited I'll just let you know not to expect anything more than tongue and nothing less than passion.
Alight girl, I'll hit you up when I have time again. I have to go get a gift for the exchange girl. Talk to you later
Hashby]
Try that one out. I know you're thinking that you don't want to make this girl uncomfortable with that letter, but trust me, it's necessary. Either she's going to start going in the direction you want or she's going to cut contact with you. Either way you win. By the way, I added a ton of DHV spikes in here for you and other tactics that are going to get this girl thinking in the right direction. Let us know how it goes bro.