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Do you mean that Sullivan should essentially be re-argued in front of the court? If so, what sort of scenario would be required to have this happen?

Yes and no. Sullivan was a unanimous decision with strong concurrences; you could not present SCOTUS with the same facts and get a different answer.
OTOH the facts of Sullivan are not typical. Mr. Sullivan was a Southern Democrat, a species now virtually extinct and not all that popular nationally even in 1964. His complaint was about an advertisement, not normal editorial content. And in 1964 there was a lot less criticism of “bias in the media” (not none at all; Barry Goldwater complained about “referees” being on the other side after losing the election that year).
IMHO the prime fact to be brought before the Court is that there are no grounds to assume that the nation’s presses are independent or objective. The reality is that the wire services are virtual meetings of “people of the same trade” - and that Adam Smith would have been only too accurate in predicting that the result would be “a conspiracy against the public.”
It has to be an antitrust case first, and a libel case second. It needs the Republican Party as plaintiff, because individually the libels of Republicans might not seem to require a change of perspective on behalf of the Court. But over the course of time, there is an easily documented pattern of Establishment journalism functioning as the propaganda arm of the Democrat Party. If a politician get caught with his hand in the cookie jar, does his party affiliation get emphasized in the lede, or buried in the middle of the story if printed at all? There is a consistent pattern; if the pol is a Republican that will be emphasized but if he’s a Democrat that will not be prominently mentioned. But I need not belabor that sort of thing on FR.
The Sullivan decision says that judges are not immune to criticism in the press, but in 1964 SCOTUS had no experience of the Thomas or the Kavanaugh hearings, and didn’t know how glad they were of it. The central character in the Kavanaugh hearing - and this is not unique in the treatment of Republicans - is actually off stage. Because the complainant testified to a “recovered” memory - and “recovered” memories are usually the result of psychoanalysis. The psychoanalyst does not accord rights of rebuttal to the target of the memory. That is, the woman who complains is a very persuasive and sympathetic figure who has been seduced into a belief which she cannot distinguish from a memory but whose memory has been modified in a process that must never be tolerated in a courtroom. IOW, “recovered” memory is the real “high tech lynching.” And it had never been an issue in 1964. SCOTUS should institute regulations which very severely restrict or ban that sort of testimony, in court - including reliance upon such in defense of a libel action.
Which presumes, of course, that such libel action is allowed in the first place; SCOTUS should allow the plaintiff to rely on the statute of limitations to “prove” his case. Nobody should have to prove a negative at a three-decade remove, so the default assumption should be that the charges are false and therefore libelous.