I think you might be overestimating your chances at the top schools. You said that you won’t have great recommendations and your academic record, while formidable, is nothing unique to the people who apply for the schools you’ve listed. You’ve also mentioned that you expect a lot of aid. You will not get it at the schools you’ve listed. You will need to be a NMF at a state school or go to a small (not Ivy) private school. Rose Hulman, RPI are examples but you want a well rounded school that doesn’t do just engineering. So my advice would be to either look at smaller liberal arts schools (possibly even religious ones if that appeals to you) or lower your expectations of getting into the top 10 schools and apply to public universities that aren’t UIUC (Iowa State, University of Iowa, UW-Platteville, UW-Oshkosh).
Unfortunately, you can’t have all your cake and eat it too. By which I mean if you even do get into one of the prestigious schools, Mom and Dad are probably not going to want to re-mortage their house just for you to go. And usually, parents don’t have $100,000+ saved up per kid just for them to go to the best school in the nation. Just because you end up going to a school that isn’t a top school doesn’t mean you won’t excel and have amazing opportunities to pursue your studies and future career.