For some reason, I really struggle to see the prehistoric nature of the predators structurally significant. In your example of abuse, there'd be some very distinct differences between the two versions, The Past and The Present (two hypothetically complete stories), and the stories would have to be twisted quite significantly to fit the wrong Concerns. But in the case of Jurassic Park, whether they have advanced gene technology to bring back creatures of the past, a time portal to bring future creatures to the present, or interstellar space ships to bring extra terrestrial predators to Earth, to me, looks like the same story of things in this park going haywire, with the concern being something else than the origin of the creatures.
What might be throwing me off is the fact that, unlike in a personal story of past abuse, in Jurassic Park, the prehistoric nature of the predators is anything but related to the characters' lives or the park -- the past they are dealing with is the past of the entire planet. It might be structurally sound encoding of the Past in the OS Throughline, where things, by definition, aren't meant to be personal -- it could be the past of the planet Earth, or the past of the entire universe. To me, it feels too broad and uncontained within the scope of what's happening on the island itself. To the characters, it's not really the past in any meaningful sense -- the dinosaurs are just something alien to us, and the alienness could be encoded in a number of ways. But I might just be having a problem with a piece of storytelling.
To be fair, the film is so thin in structure, and so thick in visuals, John William's iconic score, Spielbergs awesome directing, and Jeff Goldblum's chest hair, that I think many hypothetical rewrites could be possible. If I remember right, they started building the dinosaurs about a year before first draft, before the film was even green-lit.
It could also be the case that what I'm seeing is closer to the original author's intent Michael Crichton had with his novel, while the screenplay was taken more to the direction of the Past being the concern, with Chaos vs. Order at the core. It's been a long time since I've read the book, but I vaguely remember the issue of the "fakeness" of the dinosaurs being much more prominent in the book than in the movie, which would work very well with Fact vs. Fantasy: Hammond's efforts to build an authentic dinosaur experience turning out to be a mere amusement park ride. Mr. Wu, the genetic engineer working for Hammond, is told to have made his own creations based on what was convenient, not what was scientifically accurate. Also, in the book, I think Malcom brought this fakeness up, while in the movie, he concentrates on the aspect of chaos in nature. In the film, the fact that they've fixed holes in the ancient DNA with present day DNA is briefly visited during the ride at the visitor's center, with Malcom not opening his mouth about that specific issue, instead concentrating on more generalized remarks about chaos.