Hi!
I am actually applying to Ph.D. programs in philosophy right now myself --13 schools as well! Congrats on getting in! I was shut out last year, so I know the pressure and competition! Very well done. I hope you get into more schools and have your fair pick of them.
As someone who also has a narcissistic parent, I am afraid to tell you that "cutting off all hope of my parents loving and accepting me" is your only option no matter what you choose to do. Narcissists are incapable of unconditional love --and indeed, some go so far as to say they are incapable of love at all. In my case, I dealt with the latter --any semblance of love my mother showed me was always a trick to lure me into further abuse (love bombing, as it is called). Keep in mind though that no matter what you do, they will not change. This is a reality I had to, unfortunately, accept from a very early age, but when you break out of the sadness accompanied by this acceptance it is truly freeing.
I've been reading this book, which has been really helpful in me understanding Narcissists in my life. I wasn't physically abused, more neglected and emotionally manipulated and used.
https://www.amazon.ca/Narcissist-Your-Life-Recognizing-Patterns/dp/0738285773
It has been really helpful so far; I'm part way through.
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If you are HSP and and they are caring people, then they should be even more respectful of your boundaries. Sounds like they are just using it to blame/gaslight you. Narcissists will target their victims with abuse, and tell the victim that it's the victim's fault. Sounds toxic.
As an HSP, I found that my emotional sensitivity was used against me; since I was so responsive to others emotions and was sensitive about my feelings, those things were used to make me have to pay attention to the Narc to make him/her happy. And used by siblings to put me down.