The budget has to come first…you don’t want to be in the position where your kid has an acceptance and you and your ex say ‘sorry, we aren’t paying that’.
It’s better to tell your kid what the budget is first.
With NMF, he will be able to get a significant amount of merit money at some schools. Are the NJ schools that thumper suggested on the list?
Edited to add: Here is U Alabama NMF, NMSF scholarship info https://scholarships.ua.edu/freshman/nationalscholars/
Also look at U Florida system’s Benaquisto scholarship