Your problem, then, is convincing your parents to pay for a college other than those on their short list. If they don’t buy into that, it does you no good to apply. Plenty of kids post on CC that their parents allowed them to apply to schools x, y, and z, but they only got into x and the parents are really only willing to pay for y or z. Don’t waste your time on schools if they won’t pay for them.
But if OP’s parents would let OP apply to some highly regarded merit schools, then schools would pay them.
OP, your SATs show that have as much a shot at the tippy top US colleges as anyone in your school. It will come down to how well you write your essays and what your references say. Your chances are not “very, very low”. They’re a little higher than that. “But I think my parents will be sad if that happens, because they simply don’t believe I won’t end up in a good US college. I’ve tried telling them US college applications aren’t even necessarily about merit, and with top colleges, it’s honestly a lot about luck.” It sounds like they are trying to be optimistic. Perhaps they will be sad for a bit
My daughter’s situation is similar to yours. She is a junior. She is half Chinese (her late dad was Chinese, so I know the culture of which you speak) and although we don’t live in the US, she is a US citizen. We have an excellent, highly ranked “state” school a few minutes from home, but she would like to go to the US for college/university. Like your parents, I too don’t think it’s worth paying $60K+ for a school that is not as good as what she could get at home. It’s a matter of balancing the cost/benefit ratio. Do you plan to work locally when you graduate? Even if you don’t, if your school is highly ranked internationally, you should be fine.
Actually, Berkeley and UCLA (and other UCs) can be applied to with no support from your high school at all (no transcripts or recommendations; courses and grades are self-reported), so they should count as zero schools in terms of what your high school needs to support. The only support you need is if you are admitted and attend, in which case you need to have your final transcript sent (just like with any other university).
Would you go to Vandy or Rice over NUS? If not, it’s not worth the fight with your parents. MIT seems to be the odd school in the group if you are more interested in English or the arts.
It is so sad to know certain people think those big name institute are the top colleges in America. We have a Chinese family friend also didn’t even allowed their daughter to apply only Ivy League and big institute even she really wanted to go LAC in East Coast. Other family friend’s son was 4.0 unweight GPA and 2350 SAT National Science awards but couldn’t get into MIT and HYPS. Interesting thing was she was also waitlisted at UCLA and Berkeley. He got into
Cornell though. Have you ever seen this website College Smart Ranking. As you see there are so many smart colleges in U.S. http://colleges.startclass.com Good Luck!
@twoinanddone and @GMTplus7, Vandy and Rice both offer big scholarships (though they are obviously very difficult to get).
Actually, on his list of 11, only the 2 Ivies, MIT, and Stanford don’t offer any merit scholarships (though the UMich and UC ones won’t be full-tuition for him).
Would you and your parents consider a Canadian university like McGill? It is very prestigious, but slightly less selective than the Ivies and Stanford, and more stats-focused. It is also less expensive than most private colleges in the US, and even less than the UCs for out-of-state students. I’m not sure whether it would be separate from the 8-college limit at your school.
@twoinanddone, he wants to double major in biochem and economics/public policy. I don’t know how MIT is in biochem, but it’s fine for econ.
@aznraffe, I wonder whether you might not have an admissions advantage at schools that are NOT need-blind for internationals, or that don’t give FA to internationals at all. The schools that do are deluged, the others perhaps not so much.
I don’t know how the schools on your list fall on this criteria.
BTW, Ivies and the like seem to value 800CR above all other scores. 
McGill is a good suggestion. I would suggest UChicago and Northwestern as well for those 2 subjects (and it’s easier to double major at NU with the quarter system).
What schools are on your country’s scholarship’s approved list?
My friends abroad all know Williams/Amherst/Swarthmore. I don’t know strengths in the individual departments, but wonder if they would be acceptable to parents.
I was in the same position! Stay strong. I feel you! It gave me so much stress and anxiety!
Thanks a lot for your comments and advice, guys! Also, I’m female haha
@bouders I do plan to work back at my country, especially because I want to go into public service. My problem then is whether the US college I go to will be recognised by future employers…
@ucbalumnus Thanks a lot for the advice! Another thing I’ll tell my counsellor when trying to convince her I guess.
@twoinanddone I’m not sure… it depends on cost (ie whether vandy or rice will get me a merit scholarship, but that’s really really competitive) and whether I get a local scholarship. Because if I get a local scholarship, I don’t have to worry about cost, and I will already have a job secured for me after I graduate, so I don’t need to worry if the Vandy/Rice name is well-known at home.
@woogzmama I have considered canadian unis, actually, but I’m quite aware of the reality that a lot of people here don’t recognise canadian unis at all, and in fact, places like canada and new zealand are where rich parents send their kids to college when they can’t get into local unis. Obviously the stereotype is not universally true, but that’s the reputation, which is worrisome if I’m trying to get a job back at home. Also, I might die from the cold winters haha
@Consolation I also love the fact that MIT has a public policy minor, which really just aligns very well with what I’m interested in. I have heard rumours of some colleges favouring full-pay internationals, but I’m not really sure. And wow I really hope they value my 800CR haha
@PurpleTitan UChicago and Northwestern were actually on my list (especially UChicago for economics, obviously). But in the end, because I had to pick eight, I let them go because I heard they didn’t take many students from my country/school. As for scholarships, they don’t have an approved college list, but it has to be internationally-recognised, and I can negotiate with them if I do get the scholarship.
@bookworm hardly anyone I know understands the difference between research universities and LACs haha. I personally don’t quite prefer the LAC feel anyway, I would prefer to go to a research uni. Those three LACs are somewhat known, I guess, not by the average person, but I think employers would recognise the names
@ccctransferuc thanks for your nice words!
I was trying to get hold of my school’s Naviance data to maybe show my parents what stats from my school are like, but my counsellor doesn’t give us access to naviance until like august… which is annoying. 
aznraffe, your parents’ attitude seems to be very common among Asian American parents.
If you’d be very happy to attend your state university, what do you have to loose by applying to a few parent-pleasing long-shots? Just get comfortable with the idea of attending your excellent state university. Then, if one or more alternatives emerge next spring, you’ll be pleasantly surprised.
Meanwhile, you can try to sneak in a couple of applications to high match or low reach schools. Gather whatever evidence you can to convince your parents they won’t lose face by sending you there (but don’t argue about it). Look for colleges that claim to meet 100% of demonstrated need, then run the online net price calculators to identify the ones that might cost less than your state school.
"How should I convince my parents that my chances honestly, truly are very very low (to save them future sadness)? "
-Do not waste your time, do not worry about “saving their future sadness”, they will cope, they are adults, they made it thru the hardest - raising you! Apply where they want you to apply and few others and they will know the results, you do not have to explain a littlest peep about it. It will be all explained in your acceptances. Easy, never try to go against the flow, use the flow of life instead, it will save you lots of time and other resources that could be devoted to something very productive!
@tk21769, the OP isn’t Asian-American.
Are there many US schools that give full rides to international students whose parents can afford to be full pay? I thought there were a handful, but I don’t know how many of those are on the parents’ limited list. If OP can’t get his parents to buy in to whatever the costs of non Ivy schools are, or if they won’t permit him/her to attend any US school unless it’s an Ivy, then applying to those other schools is likely to lead to disappointment.
How about Georgetown for econ/public policy + biochemistry double major (stem would give you a bonus for admission), Wellesley, rather than Vandy or USC?
I think your odds at ucb/UCLA/umich are pretty good actually, and at the latter apply to honors college.
@austinmshauri, as I mentioned above, all of the schools on her initial list of 11 besides the 2 Ivies, MIT, and Stanford offer merit scholarships (many have big ones). Who says they have to be full-ride? The parents are saying that full-pay at many schools doesn"t make sense when NUS is a fraction of the cost, but if the cost is brought down, then they may be persuaded. Also, the OP could get a government scholarship that pays for everything.
@MYOS1634, Vandy and USC offer big merit scholarships. Georgetown and Wellesley don’t.