Actually, what I said was that your scores may be too high for some HEOP programs, and too low for others (especially some of the more competitive programs). For some schools 1000-1100 will not get you admitted because that score would be too low (Marist, Fordham, Skidmore, RIT, some of the more competitive programs at NYU, Columbia, Hamilton, Cornell, etc).
There are different criteria for different schools(each school sets their own threshold.
Absolutely true, all schools including the SUNYs (EOP) will ask for more information including an interview, once they select you as a EOP/HEOP candidate. Even then, it does not guarantee that you will be admitted because there are a limited number of seats in each program (the more money being paid by the school, the less number of seats). Remember that they choose students across the state.
For example, Columbia University is one of the major employers in Harlem as many people are employed at the university and/or hospitals. They are committed to recruiting students from uptown since it is in their own back yard.
They also have plenty of low income students with potential coming in through their Double Discovery, STEP and Liberty Partnership programs. The same can be said for NYU.
Keep in mind you are 3 semesters in; you have 4 more to go. Your best bet would be to talk to your counselor at your school to see if anyone has been admitted via HEOP, where they were admitted and what the profile looks like.