The one thing that I would add is that you have to be 100% comfortable with walking away from a school if you don’t get the merit. The possible outcome from an application by likelihood are 1) rejected 2) accepted with no/little merit and 3) accepted with large merit. 1 and 3 are easily. #2 can cause an issue when you actually have the acceptance in hand. It is easy to say now that you will turn it down. If you actually have an acceptance letter in hand from U Chicago, one of the decision makers may start to waiver. The likelihood of #2 happening is probably 20x+ the likelihood of #3.
You may want to put it in writing that if accepted at school X and merit not greater than $Y then we will decline the offer. All parents and the student should sign it before an application is submitted.