Let’s get the cruelty out of the way: For many of your reaches, odds for any high-achieving student will be 95% or more that they will not be admitted RD - not because of anything lacking in their application, but because of the very few spots for very many outstanding candidates, such as yourself.
With ED you can improve those odds by a meaningful degree for that one college, but even then it will remain a long shot. But you realize that - that’s why they are reaches for everyone!
As far as Barnard, political sciences is indeed one of their larger majors:
https://polisci.barnard.edu/course-requirements
next to Economics, English, Psychology, Biological Sciences, Neurosciences, History,…
I think your GPA and class standing, especially in light of what appears to be a resource-limited public high school, social-economic background, FGLI makes you appear as a young woman with great potential and persistence.
And the consistent activism shown through your various EC’s, while maintaining a part time job and teaching music at a middle school, further hints at the type of exceptional young woman that Barnard hopes to attract. Your essay idea will further support that.
Assuming that Barnard will be test optional, you might have to weigh whether you already have sufficient factors in your favor, where whatever SAT score may (at best) not truly add to it.
Wishing you good luck on this journey - you already have done very well for yourself!