I think you're really over complicating Arya's inner workings, in that context, and giving her far too much credit. She simply wanted revenge and we have no evidence, that I'm aware of, that she gave the first two kills a whole lot of thought. The first, the tickler, seems to be more a reactionary response than a contemplative one, and this fits with her character, especially in that moment where she's still figuring shit out and how to deal with the new world she's been thrown into.
She's not even thinking about escaping until the final kill(s) (the only one, I'd argue, that is contemplative at all). The second kill was a fuck up on her part by trying to do too much too fast.
In short, I think she messed up a LOT. I'm not saying this is a problem with the writing; it's not. It does fit with her character but it's a monumental fuck up on Arya's part to not walk out of there with at least one major kill.
Though it's hard to fault her a whole lot I suppose, because like I said, she's still very young and new to surviving on her own, let alone understanding how the game is played.