The problem is this: unless your child is given an entitlement need based grant (like Pell), there probably won’t be stacking of NEED and merit and this is why…
Merit is applied first, then the school looks to see if there is still “need”. If there is no need, then there won’t be need based aid.
here are some exceptions:
Student EFC 1000…qualifies for some Pell…Student gets several merit awards that are allowed to be stacked and they meet COA…Pell will still be given on top…and it will cover that EFC.
Student EFC 4000…qualifies for some Pell, …student gets several merit awards that when totaled, meet need, then about 3000 Pell is stacked on top, cutting into EFC and leaving only 1000 to pay
These scenarios only exist because Pell is an entitlement. Students get it whether there is need or not.
You seem to be looking for a school that will give need based aid, and then will allow you to add merit to it and reduce your EFC. Schools don’t let you do that because they view that merit as reducing your need.