Fellow Japanese here, with a friend in a similar situation.
If you can’t bring test scores up, you might want to consider test-optional schools: http://fairtest.org/university/optional
You may also want to consider Questbridge, which has a significant number of options for non-citizens, depending on the school. We don’t know what your family’s income is, so I cannot say for sure if this would be a good option.
I’m not familiar with how exactly the green card/permanent residency affects college admissions, but if it does so greatly, I would also think about taking a gap year just to wait for the green card. There are great things that you can do in that time (service, work experience, etc)!