Agree with others either no going to other islands or go to only one; my vote would be Anguilla.
One beach not on your list that is semi-secluded is Anse Marcel. It's a dramatic drive to get there with beautiful views along the way. One of the best beach restaurants on the island is Anse Marcel Beach Restaurant on opposite end of Secrets. Water is usually quite calm and great for relaxing. It's my favorite beach on the island. (As a point of reference, I am not a fan of Mullet Beach.)
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