I'm with you. I'm a HSP too. And one result is anxiety when ever I get overloaded with noise or crowds or frustration at trying to solve common problems and hitting obstacles. It is not pleasant. But every experience I've found has its positive and well as negative sides. For me, the positive is an ability to concentrate on issues very intensely and to pull up insights through intuition. I'm also quite introverted and tend to drift off into an inner realm where I get information from somewhere in pictures and dreams.
I deal with this by needing to spend a lot of my day in solitude. I need the alone time to recharge and calm down.
Thanks for this post, by the way. I am not a meditator now, but I've used that approach in the past to get grounded and stabilize my centeredness. It certainly helps. Now, I have other ways, including the ways Epicurus taught us about. Experience I found was a good way to learn how to live as well as philosophy.