It’s a good thing you are a Jr because you have some time to learn a bit more. Your parents have the right idea and their requirements are good ones that don’t put you or your family too much in the hole.
When you need a lot of aid, you don’t pick the school first, you look for ones that give the aid, then you pick among those. Because some schools will simply be unaffordable. Not all schools will ‘meet need’. So you will get your federal aid, which is a little and that’s it. The rest your parents will have to pay, and they cannot if you are low income. Don’t maximize your chance of going to these schools but rather find schools that will cover your costs. Well you can apply for Gates Millenium and see if you get it and use it where you want. You should not be narrowing down options, you should broaden them to schools you can afford
Your first assignment is to read the posts pinned to the top, in there will be a Financial Aid FAQ which will familiarize you with some concepts.
Every US citizen and permanent resident qualifies to fill out FAFSA. Are you saying you are Pell Grant eligible? What is approx family income?
Do not neglect to apply widely for instate where you will get aid. If you are UC eligible, they give the best aid for low income. At least if you have full tuition somewhere that can be one of your safeties. College is not an extension of high school, that is simply immature hogwash. Only immature students treat college like HS. You don’t need to copy anyone else who does.
The CUNY – like Calgrant instate, CUNY students get TAP from NY. You don’t get that, so likely you are full payer.
Fordham, Pace, St John - don’t meet need. It is possible you could get enough at Fordham if you are a top student.
Barnard - meets 100% need, so if youf family can pay the portion they deem you should, then you are good
MI - don’t expect anything from the state ones you mention. I don’t know the others
I suggest you keep exploring colleges and run the Net Price Calculator for the ones on your list. When I help kids I usually make a spreadsheet that shows extra costs that aren’t in the COA, like extra travel and other expenses will be more in NYC to CA or MI to CA. Also CA colleges include health insurance in the COA and most other ones don’t, so if you have to buy health insurance that can add 1,500 to 3,000 per year depending on the college, you can find that info on the website.
Did you visit USD to see what a college similar to Fordham would be like?