If you think you’ll get your green card before the next admissions cycle, then a gap year could be the way to go.
Does the public you could commute to allow accepted students to defer admission?
If I were in your position and had reasonable certainty that I’d be able to apply with legal residency the following year, I think I would file only a small number of applications this year:
- The public flagship you can commute to
- Washington & Lee, in hopes of landing the full-ride Johnson Scholarship. (Odds aren’t terrible - they give it to 10% of accepted students. Geographic and racial diversity will help (I don’t know that they officially count Asian students as URM, but their student population is under 4% Asian so it’s at least an unofficial plus), and your stats and other qualifications certainly make you a strong candidate.
- Anyplace else like W&L where you’ve got a decent shot at big merit.
Then, you see what you’ve got when the decisions come in, identify your best plan among those choices, and see what happens with the residency process. If it’s looking like your green card still won’t come through before the next cycle, just get started with college in Fall 2023 and leave your super-elite aspirations for grad school. If you do think you’ll have a green card to apply for Fall 2024, then weigh whether you want to take the gap year. If you’ve got a full ride under your belt, you still might want to go with that. But you can consider it, run the NPC’s (which at least will be applicable at that point) and compare the affordability of full-need-met elite private U’s with the options you have.
IMHO, this plan would be better than applying now to all of your most-desired schools, and then having to REapply after a change of status - having been rejected once could be a less advantageous position to be in than being a first time applicant.