Yes, with a 92% rejection rate (8% acceptance rate), Rice is a lower probability. But you have outstanding credentials so it’s worth a shot - especially since it’s your first choice.. I’ve seen some admissions surprises there, which I attribute to their holistic review. The essay(s) is important, and it’s important that it be authentic and that it be in your voice. References are also important.
Applying early is important at Tulane, but Holy Cross has also been known to favor early applicants in recent years as well and I wouldn’t take admission there for granted. They have become highly selective in the past couple of years. I would agree with your characterization of Trinity as likely and I would, OTOH, consider Baylor and SMU to be very likely.