If you feel you’re assured of entry into Rutgers, that’s your safety. Personally I’d add a second. I think you’re good but crazy stuff happens.
Check those others to see if they offer total merit scholarships because if they don’t then why apply ??
Find a school with a Stamp Scholar or other full ride like UNC, UVA, W&L. At Wake look at the stamps and Susan Reynolds - see what is required to get - bcuz that’s how you can afford, etc.
Always ensure you have a possible way to afford or it’s wasting time applying - if that makes sense.
So in that sense with the two scholarships I just noted WFU could work ( although Winston Salem is not remotely NE) but see what you need to do to get those two. Check out the Fredrick Douglas at AU and Johnson At W&L too.
Good luck.
Ps there are other lists but this may help you narrow in on funding oops ( I see Fordham on there, for example).