She does not require several thousand strikes from an individual weapon. After thousands of interactions, she simply has a vast library of enchantments to rely upon. She has interacted with the staff on at least 8 occasions. Usually three is the number I use. 

Edit: Earlier in the fight, she even says she'll need a 'few' more tastes. This is after she had already interacted with it.

Edit 2: I never enforce my laws upon other people. That means I will never outright declare my weapon is superior to another. Corban merely deems his superior. Besting enhanced weapons is entirely a process of her interacting with them and nothing more.