How to balance numbers of schools vs casting a larger net for best outcome (admission/aid)?

We visited a couple of the reach schools when in the area, but left the rest to see if she got in or not.

One of her matches - Tulane - says interest is really important but it’s far from us, so she never went. She got in EA with a terrific financial aid + merit package. Unfortunately, a technical issue on their end prevented us from getting that package until mid-April and by then she’d decided on a different school.

Point is, Tulane understood we don’t live near and visiting without knowing if she could attend would be a hardship. She expressed interest with an EA app, a very thoughtful “Why Tulane” essay, and an email or two to her regional rep.