Rice parent here. I agree with others that you have a decent chance at Rice ED if you show some interest (attend webinar/visit campus if possible), probably better than the published rate of 15%. As an Asian male interested in STEM, you’re in a very common demographic basket for Rice applicants, but ED will reduce that competition somewhat and I would guess that your ECs may be a bit stronger than most. Also, the share of domestic students in the student body from outside Texas has been edging upward, though I don’t know if that emphasis is enough to improve the chances of any particular applicant.
We don’t have a lot of financial info here, but I would suggest applying for financial aid, even with income of $200k; Rice has very generous need-based financial aid and might provide a small grant that would help your family bridge the gap between EFC and your actual ability to pay. Our family’s EFC was 35k, but our Rice grant actually brought our net cost down much lower than that.