RE: “It was reported in the NYT that he told a top aide that, but no report of it on the record or via recording.”
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Yes, it was in a New York Times article on April 25, 1966, referring to an unnamed source.
The author linked below says that he could not find any reference to it that pre-dates the NYT article.
https://www.gizmodo.com.au/2017/03/the-story-behind-that-jfk-quote-about-destroying-the-cia/