That said, the game is over.
That having been said, the game is over.
That being said, the game is over.
Are all equally acceptable?
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All three are acceptable.
That said — Wiktionary
"Christmas is exploited by capitalism. That said, it is still a religious festival."
It is a set phrase, kind of idiomatic.
Synonyms: Be that as it may, Having said that, Nevertheless, That being said
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.
"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.