Check out this article:
Meeting Girls in Messy Situations / Friends Around
In particular, skim down to the section titled "The Girl Locked Into a Big Group." Your options in the scenarios you've outlined are the same - either you wait for her to wander off somewhere alone and sneak out to go meet her then, or you weave your way through the group until you're right next to her, build a quick connection, then make a casual exchange of contact info.
If you get into a decent chat with her and the other folks approve of the match (or at least don't disapprove), they typically will not interfere. You and her might both get questions about it later, but if you keep it relaxed enough and you're sociable with everyone else, you'll each be able to play it off as no big deal and meet up later without the social pressure on.