First thanks for the reading. I'm still enjoying it.
Second, I can understand this girl, because as AvPD myself I have tried (sometimes forced) communication this way with people.
And why I say I understand her? Well: because she is probably aware of your PD if you told her, even if you haven't she'd probably notice after all the time you spent together. I, like her, am able to communicate through messages; not just to keep in contact with the world but also to understand if my thoughts are acceptable or if I'm a complete mess after all. So the fact she is nice to you online doesn't mean she doesn't hide some distrust of your intentions, being them more or less clear to her she may even have perceived rejection at some point (and forgive you in silence at the same time), but STILL she knows that if something happens on the online world (like being actually rejected) won't affect her as much of that on the real world. And the real world is the BIG thing, it's the risk and that's probably what she is dealing with right now: "should I take the risk or not take the risk?"
I don't know if you told her about your intentions of agreeing to see each other once in a month and stuff BUT that is probably not the answer for her desires. Well it may be the best thing for you knowing your conditions, but imagining how she feels [and I felt like her so many times, jeezzz] that is possibly (99% sure) what she never idealized of how to be in a relationship, so she rather stay with you online a.k.a. closer than having you close but not close enough BECAUSE she already knows your limitations AND she WILL be hurt sooner or later. Sooner than you'll be able to notice I assure you. Someone with AvPD needs constant attention and a sense of normal life, which is possible and achieved when the person feels like a common human being with no more reasons to run away.
All these words to tell you that I don't believe your case is a material-izable relationship; still I like the way you described how important it is for both of you.