Both sides in this case were utterly contemptible. I would have found that Gawker invaded Hogan's privacy and awarded Hogan one dollar in damages, leaving everyone unhappy but the lawyers. Invasion of privacy, despite its questionable origins, is now generally recognized as a valid tort and outside of the protections of the First Amendment. No new precedent is being set here.
I don't think Bollea is a particularly good person, but I'm not clear on how his conduct in this controversy was "contemptible". For the 1A concern here, consider the Anthony Weiner case, in which indisputably private photos of Weiner were also published. I don't like that they were (I think he could have been just as effectively ejected from public life with good writing) but it's concerning to think that he'd have…
That good writing can mention that the author has seen the photos or videos, and describe them as necessary to support the story.
Of course, if the photos and videos are not published the subject might accuse the publication of lying, but the original publication can show the photos or videos to other publications who can also write stories about them.
In a case like Weiner's, I don't think the public would believe him if it came down to several major newspapers all reporting that they had seen the photos first hand, versus Weiner saying that they are all lying.
If the subject tries to sue a publication over their written story, the photos or videos will be evidence for the defense, and the likelihood of them getting out to the public goes way up. That should provide quite a bit of discouragement of intimidation lawsuits.