It may or may not be too late - can you take AP Calc BC senior year to have it on your high school record? Can your parents override the teacher “non-recommendation”? Otherwise, it would be hard to justify such a gaping math hole in your transcript. Of course, if this is not possible at this late date, then move on, but I feel it’s worth exploring.
Here’s my detailed reasoning as to why this may be at least worth considering: I am not sure you can count on a school counselor’s letter to substantiate the reason that you have stated for not being able to take the school’s Calc BC . And self-study and taking it somewhere else would not carry the same weight. Keep in mind you are competing with others who have all this on their high school transcripts. Again, if it’s not possible to change your schedule, then move on and work with what you have.
What was your math course for junior year? AP Stats is considered an elective, and not a strong main math course for a STEM student aiming for competitive universities. Also, was the AP Physics 1 or AP Physics C? Does your school offer the latter?