I'd go with 1. Impress on her that you'd kill for the opportunity, and tell her why, but tell her from a company-centric point of view. "I bring X experience and I think I can create value by Z. I thought it was odd that I had been screened out by the portal and when you followed up it reinforced my feelings."
if you get caught in a lie you're cooked. it's possible you might get away with it but if you don't you get her caught up in your BS and that's a spectacular way to make an enemy.
you've just always got to be honest, IMO.