Stony Brook at $20,000 per year is your only realistically affordable option that does not involve transferring. You would have to take a federal direct loan of $5,500 and earn about $3,500 from work to cover the $9,000 remaining after your parents’ contribution. But Miami at $28,000, GWU at $30,000, and UIUC at $50,000 would require parent cosigning loans or parent loans, generally a bad idea for both you and them. And Stony Brook is a well respected school anyway.
The Queens-Columbia 3+2 program may be affordable at first, but admission to Columbia requires meeting strict grade and GPA requirements, and Columbia does not promise as good financial aid (need-based only, no merit) for 3+2 transfers as it does for frosh and other transfers. However, if going directly to Stony Brook is still too much of a financial stretch, you can start at Queens and attempt to transfer to Stony Brook (or other SUNY) as a junior to finish your engineering degree. But that entails the added risk of not being admitted to an affordable school as a transfer student.