There are a bunch of great schools that offer merit aid. Just keep moving down the list from elite to excellent to very good until you find one that loves your daughter enough to meet your price point. But honestly, if you’re going to play this game you must embrace the idea that there is no single perfect school for each child. Visit a few, figure out what DD likes and then go find one like that that you can afford.
There’s a very good essay on the Muhenberg College financial aid page ( http://muhlenberg.edu/main/admissions/therealdealonfinancialaid/ ) that more or less says schools use aid money to “buy” the type of students they want to attend, so your best approach is to apply to schools where you’re a desired student. Aim for places where you’re above the 75 percentile of incoming freshmen, for example, and they’ll be more apt to try to lure you in.