[Current HS Senior] Will be attending a non-target school this fall. Need advice.

edit: sorry for the really long post. I would really, really, really, really appreciate any advice, though.

Hi, I am currently a senior in high school, and I will be attending a non-target state school with pretty much a full ride. I am on the East Coast of the USA. My goal is to get a job on Wall Street.

I am going to use the first paragraph below to talk about my experience/credibility and the paragraphs after that to ask some questions. However, I am very new to finance, so any comments/advice (even ones that are seemingly unrelated) is appreciated. Note that some of what I have stated below may seem vague. If you would like to ask any specific question(s), you can send me a private message.

In high school, I took several math courses including AP Calculus BC (equivalent to Calculus I & II), AP Statistics (intro-level statistics class; no calculus), Multivariable Calculus, Differential Equations, Linear Algebra, Complex Analysis, Real Analysis, and Discrete Math. Also, I'm not sure if it SATs matter after high school, but I received an 800/800 on the SAT Math section, and an 800/800 on the SAT Math II Subject Test. I have been interning at a research lab, and I have co-authored a research paper on stochastic processes. The paper is pretty much all applied math. I am pretty good with MATLAB and R since those are the programming languages that I have been using at the research lab for >1 year. I have also taken many AP exams, which will grant me college credit.

So, first, I am conflicted about what to major in. I e-mailed the math advisor for my university, and given my math courses, I would be allowed to take upper-division and possibly graduate-level math courses beginning in my freshman year of college. I could probably graduate in two years as a math major. I am a little bit reluctant to major in finance, because if I don't make it where I want to be, I have little to fall back on. Additionally, the finance major at my college has very few math requirements, so it would be difficult for me to graduate early. Alternatively, I was thinking about majoring in Electrical Engineering or Computer Science, both of which are fields that interest me. These would also allow me to have a fallback plan. It would be fairly easy for me to double major in math and some sort of engineering or computer science since I have many math prerequisites. I would definitely be involved in extracurriculars related to finance, but I'm not sure if that compensates for not majoring in finance? It would also be kinda difficult to double major in finance and something as back-up since there isn't much of a coursework overlap with like Finance and Electrical Engineering.

I could also try to transfer to a target school after my freshman year or something. Unfortunately, I was rejected/waitlisted from the reach schools that I applied to as a freshman applicant, but I would be willing to try again. Would this be a good idea?

How can I get internships from a non-target school? Through some quick Google searches, I found that it's pretty hard for a high schooler to get anything, but what about after my freshman year? My school won't have on-campus recruiting, so it might be difficult, I think.

I'll edit this post if I come up with any more questions, etc.

All comments are appreciated.

Thanks!