Andy, if she wont do it then maybe you should let it be for now, after all she sounds real, nonchnlove photos and you have and have used her phone number.
I would wait for a month or two and then ask her if she would give you a webcam date so you could see and hear her sweet face and voice, so you can dream of her this night.
Do it this way or some way like this and she will most likely do it for you and in that time frame she will get to know you as a person, right now you are letters and a voice, give her time and don't push to hard or you may lose her, of course this is just my opinion.
Good luck and best wishes