Only SCU can give you definitive answers. Are you renting/living in a non-owned property now?
Again, SCU doesn’t meet full need, so this could be the most your S will receive. Although I am curious why their NPC estimate was off…did you keep a record of that? Most schools don’t meet full need, but it’s fair to talk with SCU and make sure they are understanding all the pieces. Then, they either give more money or they don’t. How far off is the offer from what you can/will pay, without taking parent loans?