Should I give up on American universities and settle for a uni in my home country?

Consider Japanese universities your safeties.
Then, add other universities of interest that are within budget - those could be universities in the different countries you’ve lived in, or universities in Canada, Australia, or Europe that offer programs in English.
For instance, if your stats basically guarantee you admission to Japanese universities and you’re aiming for Top50 universities/LACs, you likely have the stats to get into McGill, Waterloo, UToronto, and/or UBC.
Then you could try your luck at a variety of American universities, understanding that if they don’t come within budget, then they’re out for you.
Consider in particular universities that guarantee a full-tuition grant for students whose families make 125K or less, such as Rice. Since you’d apply as an international student, you’d be among an insanely competitive pool, but it’s worth a try.
At Cornell, look into ILR or CALS rather than CAS or COE.
Oberlin is going to be very, very competitive too. Basically any university and LAC within the USNWR Top 50 is going to be very competitive for international applicants who need a lot of aid.
However, since you’ve prepared for so long and have a strong background making it possible that could get in, I don’t think you should give up now. Simply keep your odds in mind, have several Japanese universities or international universities lined up so you have a choice, then carefully choose a variety of US universities.
BTW did you graduate in April, will you graduate in November, or will you graduate next year (April or June)?

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