Independent Study for Credit

I’m going into my junior year but have been planning my senior year courses. My school does 8 periods, and I know that I will be taking at least these 6 classes.

AP Lit, AP US Gov, AP Chem, Journalism, Journalism work period, science research project

For reference this is my junior year course load. The reason I’m self-studying AP Bio is to qualify for a certain summer internship.

AP Lang, APUSH, AP Physics 1, Journalism, Journalism work period, AP French, AP Calculus BC, post-AP CS, AP Bio (self-study)

The only other AP courses at my school that I have not taken are APES, AP Psych, and AP Stats. The problem is that I don’t think AP Stats will prepare me for for college math, and APES and AP Psych are known to not be very serious academically.

Looking at the course catalogs for some advanced high schools, it seems relatively common to teach all of AP Physics C in a year, as well as to offer a combined course in multivariable calculus and linear algebra. I believe that taking these as my 7th and 8th classes would best prepare me for college.

What I wanted to do then was to independently study these courses, but have them appear on my transcript. I could technically only take 6 classes my senior year and still have enough credits to graduate, but I want colleges to know that I took them.

I mentioned taking an advanced math course my senior year, and my counselor suggested that I would have to find a teacher at school to serve as a mentor and make sure that I was doing the work, and I know a teacher who would be willing to do that.

My plan of study would be as follows:

Physics C: Mechanics
1st semester
University Physics (Young and Freedman)
MIT OCW 8.01

Physics C: Electricity & Magnetism
2nd semester
University Physics (Young and Freedman)
MIT OCW 8.02

Multivariable Calculus
1st semester
Multivariable Calculus (Stewart)
MIT OCW 18.02

Linear Algebra
2nd semester
Introduction to Linear Algebra (Strang)
MIT OCW 18.06

Is all of this feasible? Would my counselor let me? Would colleges be impressed? Would it be worth it?

I am good at self-studying: I spent 50 hours studying AP Calc AB and got a 5. I would most likely retake these courses in college, and I do have large extracurricular commitments. My goal is to study the intersection of computer science and molecular biology at schools like Princeton and MIT.