They can keep the basic plot in tact, but I would 100% eliminate Lily Potter from the show. She serves no purpose, and it would shorten the opening scene considerably.
The time turner would still feature, but after Harry finds it, Delphi steals it (off stage from Hermione's office). Instead of Albus and Scorpius trying to save Cedric, they'd be trying to Stop Delphi, and end up getting kidnapped by her and taken to Godric's Hollow. It'd really be a combination of Part 1, Act 1, and Part 2, Act 2. Delphi would be about Harry's age, because instead of being the daughter Voldemort, she is still the daughter of Belatrix (and her husband), raised by two death eaters because her parent were imprisoned. No rumors about Scorpius being the son of Vodemort,but still ostracized because he is a disgraced Malfoy. They'd be able to eliminate all of the flashback scenes, Harry's scar nonsense, no Dumbledore scenes, no "general meeting" scenes, and no alternate timelines. I'm sure there's a way to keep the dementors. And no rightous indignation speeches from McGonnagall.
It'd still be long, and some of the spectacle might be lost (such as the bookcase and even the polyjuice potion), but they can can still keep the old wizard's home, the dementors (somehow), and even duel between Harry and Draco.