Just remembered this.
My father in law has high arch and suffers from other feet problems. For him, the regular dock side shoe is very unconfortable.
So he went to a tennis store and bought a pair of NIKE shoes, (I believe )whose sole was specifically designed for grass tennis courts. They are perfect as the tennis shoes soles have a "brake" design at the bone behind the big finger (I don't know the name, so call me stupid), (ball of the foot??), and have excellent grip.
Now the beauty is that inside because they are designed for hard impact on ground, the arch is very high.
The downside is they are leather and it was not made for sae water. But they make them in cloth, too.
Hope it helps, he is very happy. I had forgotten about him.