One thing to keep in mind is there are a multitude of instances where colleges provide full need to students, even when that college does not “guarantee” to meet full need for every student. Not many universities have the endowments necessary to guarantee to meet the full need of every student, but many colleges agree to meet the full need for a few students a year as they see fit and can afford to.
I say this to encourage you to not limit your applications only to schools that guarantee to meet full need. With some research, you can identify schools that provide good FinAid to students without being labeled as “Meets Full Need”. Those are a good place to widen your scope.
Every student in the world who has significant financial need is choosing the same tiny group of Meets Full Need schools to apply to. That results in an even lower acceptance rate for students with need who apply to those schools, than those schools already list. If a need aware school has a 22% overall acceptance rate, you better believe that the acceptance rate for students with high need is going to be much much lower. By targeting only those schools, you are already diminishing your odds.
Apply to some, certainly, but also go against simplistic reasoning and go against the grain a little.