I'm with you about being optimistic here *g* I do think it'll take time before Ginny would be willing to meet Snape, let alone getting to know him in a more personal level. But I've always interpreted her canon characterisation as being someone who's strong and independent, but fiercely loyal and family-oriented. Snape doesn't really have anyone besides Eileen and Harry this time around, and Ginny's Gryffindor sense of fairness would compel her to at least make sure Snape's doing okay, opening the door to developing a future rapport.
Eileen is fast becoming one of my favorite HP characters. Despite the inevitable arguments/bickering I see between her and Severus looming in the horizon, I daresay both of them would be much happier now :)
I'm glad you liked this enough to share with Mr. whitestar! *blushes*