A large upward trend resulting in a 3.1 cumulative GPA means that your earlier grades had to be C’s and below. Competitive-but-holistic colleges are often willing to forget earlier stumbles followed by strong improvement, but this sounds like a lot to overcome when aiming for colleges with single-digit acceptance rates, where and overwhelming majority of accepted students are at the top of their high school classes. What is your college counselor going to say in your recommendation, about any extenuating circumstances in the earlier part of high school?
Why are you singling out some of the most difficult schools to get into? If it’s because you need the most generous financial aid possible, then RIT doesn’t fit the pattern. But there are schools that do meet need and aren’t as ridiculously hard to get into as Harvard and Princeton.
It may be that UNM or one of the other New Mexico publics ends up being your best option, and you can get a great education at one of these. What don’t you like about them? Is it that you want to go farther from home? Is it that you think you’d be happier at a private university rather than a public one? Is it that the aid at the top privates is better than what you’d get at an in-state public? Is it just wanting a famous school that everyone has heard of? What’s driving your decision tree?
Have your parents run Net Price Calculators for the schools you’re already interested in? Since you’re hoping to go somewhere with need-based aid, you and your family should familiarize yourself with NPC’s and run them for every school you consider. Plus, it would help commenters here to know your actual budget - what UNM would cost for you, and what elite schools like Harvard and Princeton would cost if you were to get in, and what costs would actually be manageable for your family. (You note that these schools are “tuition free” for lower-income families, and this is true, but non-tuition expenses can still cost upwards of 20K/year so “tuition free” doesn’t automatically equal affordable, for a lot of students.)
Once you have that info on the schools you’re already thinking about, IMHO, you should try running NPC’s for some still-excellent but slightly-more accessible schools. For example, try running the numbers for Trinity University in San Antonio. It would be a change of scene from NM but potentially driveable. Trinity offers multiple engineering disciplines, and physics, plus an established pathway to double-major in physics and engineering science: https://www.trinity.edu/academics/departments/physics-and-astronomy/double-major-roadmap They meet full need, and admissions are need-blind.
Others to look at could be Lehigh (no-loan financial aid for low-income students), Lafayette, Case Western Reserve (check out their ABET-accredited Engineering Physics major Engineering Physics, BSE < Case Western Reserve University) and U of Rochester. And since you’re female, check out Smith College also. Smith College | Engineering Smith has strong physics and engineering in its own right, and you can also cross-register at its consortium partner schools including UMass Amherst and Amherst College.
To be clear, I’m not saying that any of these would be an admissions slam-dunk for you. A mixed profile like yours is always a judgment call for colleges, and nobody here can predict how that will go. But applying to some schools that at least have double-digit acceptance rates (but still offer generous financial aid) would be a step in the right direction.
The thing is that, as tsbna says, there are some full ride or nearly-full-ride scholarships available for NMSF that could be far more advantageous for you than relying on need-based aid. U of Tulsa will give you a full ride even if you don’t make Finalist (not a problem for most semifinalists, but I’m unclear as to whether your grades could make that not a sure thing). Tulsa is a mid-sized private university; if Ivies appeal to you, then Tulsa might as well. They have engineering physics too… and if you’d have any interest in continuing your Spanish studies, you could look at their International Science & Engineering program, which is a five-year dual-degree program (fully funded for you) where the fourth year would be spent abroad in a Spanish-speaking country. (One semester of academic classes, plus a full-semester internship.)
Other NMF scholarships to look at would be those at UT-Dallas, U of Alabama, U of Alabama Huntsville (smaller and more STEM-focused than the Tuscaloosa flagship), U of Central Florida, and U of Maine. Engineering Physics
I don’t think a “Harvard/Princeton or bust” approach would work out well, but there’s no harm in a few super-reach applications as long as it doesn’t divert energy from applying to less-rejective schools as well.