If you have a suggestion as to how to match hundreds, if not over a thousand, girls with 10 or more sororities in a week's time I'd love to hear it.

I don't want to sound snarky - I just honestly have yet to hear of a better way.
The system, flawed though it is, is the best we've come up with so far. The new release figures have done a wonderful job of helping match each girl with a sorority home - and yes, you are right, it doesn't always work. I will point out that it worked out for your daughter, and even had she been placed with her other pref group it might have - we have many threads in our recruitment threads that have that exact scenario, and many of those who didn't think they would click found that they were actually where they were meant to be.
Formal rush is really a very intense experience. I've posted elsewhere that my daughter will not be going through formal rush because she and I know she would not be comfortable with the hot-house environment of recruitment. I hope she is able to find a home through informal recruitment, but who knows.
I think the NPC has done a great job of trying to address concerns about recruitment. And I would be very surprised if they weren't always trying to think of ways to improve the three types of recruitment they currently recommend.
I'm so glad your daughter had a happy result. Hope she really enjoys her new member period.