1) That is NOT the formula used in the Net Price Calculator for the Ivy League schools we considered (ONE Ivy League university for my daughter and several for my son who would have gotten in for sure based on his athletic abilities - though he was still a stellar student, but he would not have been guaranteed admission if not for the athletic part). My daughter did NOT end up going to an Ivy League school. She instead went to another elite university with similar aid.
2) As we were focused on paying the least possible, I was mostly concerned with doing that. We got rid of liquid money (more than what you are suggesting there) and got the best deal we could based almost solely on our income.