"That said," "That having been said," or "That being said"?

"That said" is an appropriate truncation of "that having been said", which is correct in that the clause refers back to what was just stated in the prior sentence. "That being said" is incorrect since the prior sentence is in the past. It is not in the process of being said. That said, "that being said" is still a commonly used idiom.

if something is said before something else, then "that having been said" is correct, while "that being said" is not. "that being said" means something is being said in the present, whereas "having said that" places the "saying" before the next phrase. regarding the examples below, "being in prison" is different from "having been in prison." "Now that is said and done" means something is currently said and done, like "do Americans say the word elevator and ride in a lift." Now that was said and done would suggest in the past, Americans said elevator and rode in a lift.

David Pearce is absolutely correct. In fact, “That said”, “That having been said”, and “Having said that” are all equivalent and have been around for centuries. “That being said” is a monstrosity that incorrectly shortens “That having been said” and arose out of the blue in the last couple of decades. Of course, like a lot of linguistic monstrosities, it has promptly spread like wildfire, and even people who wouldn’t have dreamt of saying it in 2000 are dropping it every five minutes in 2020. And yes, “being said” implies simultaneity, while “said” alone is a past participle and synonymous with “having been said”. Bottom line: “being” is incorrect in this phrase, and so is anything beginning with “With”, i.e. “With that being said” is a double monstrosity.