I’m not aware of the small print at the different schools. How many state that they offer a limited number of NM Scholarships? How many want you to designate them as your first choice before you SIR?
Here is a link to last year’s thread. I don’t remember anyone running into the problem that you mentioned. @amsunshine knows quite a bit about NM but she hasn’t posted since her youngest graduated high school.
My child who was a finalist in 2020 is at USC. I have first hand experience with USC and am happy to answer questions about the USC NM program.