I would also look at the Robertson Scholarship info…
It is highly competitive and might not make sense to expend the extra effort to fill out the separate application but you should be aware of it for both Duke and UNC.
Here’s the FAQs. Note I don’t see it here but some schools will asterisk something such as - assuming expected assets. In other words, substantial assets, regardless of income, could impact. I don’t see it here but if your family has substantial assets, you might ask.