The college is NOT going to give you money to pay your calculated family contrition. So forget about that.
In the example you give, the balance left to pay is $13,500. $7000 of that is the expected family contribution which you will be expected to pay.
You haven’t answered THE most important question we have all asked…over and over and over. Does this college guarantee to meet full need? If not, you probably have gotten all the aid they will be giving you…so your net cost in your example is $13,500 and it won’t likely get reduced.
There are tens of thousands of people who are asking colleges for additional money right now. What makes your case more compelling than someone else’s? Did a parent die? Does a parent have a terminal illness that prohibits them from continuing to work? Really think about it…the “I just can’t pay that much” reason isn’t going to fly anywhere. And there will be people in far worse financial shape.
If you can’t afford this college…find one you can afford. Or have your kid go to a CC, or take a gap year and try again.
By the way…if you were going to receive SEOG, it would have already been given to you. It’s for lower income students and there is limited funding per college. It’s awarded on a first come first serve basis. So…those filing their applications on October 1 will be in line way before you. Same with federal work study. First come first served.
When did you actually submit your financial aid application forms?
What makes you think you should be getting more aid than what you got…except your misinterpretation of what you thought the federal government was supposed to give you?