“So I’m hoping, even if they give me poor aid at first, I can liaise with them to try get a better deal.”
Financial aid offices, at most US universities, don’t work that way. They budget the financial aid packages over the course of four years given expected rises in tuition. The universities have limited financial aid budgets. In other words, the funding dollars are finite. You get what you get from the initial offering. You can’t “bargain” your way to a better deal in subsequent years. Every student would be doing that every year who needed better financial aid.
If your your family income changes significantly, then you would have to provide written documentation of those changes and they might adjust the aid but that’s not guaranteed.
Wherever you get in, with aid, then you should assume that that’s the aid that you will get for the remainder of the undergraduate education.
Go in with the understanding that you may or may not get sufficient financial aid for certain schools. Every school is very different which is what attracts so many students to US colleges and universities.