Instead of having Pettigrew revealed to Sirius, Remus, Ron and Hermione, Harry chose to immobilize the rat and stuff him in his pocket - on the off chance that both Remus and Sirius were telling the truth. Afterwards, Sirius helped get Ron on a magical stretcher and they sent Hermione (with Ron) ahead of them up to the castle. Harry and Sirius debated what to do with Severus, and decided, ultimately, to leave him there. As they headed up to the castle, Remus transitioned to his werewolf self - endangering Harry. Sirius transitioned to his dog-self to help save Harry, Severus woke up and came out to the fight between dog-Sirius and wolf-Remus and shielded Harry.
When the wolf-sounds and Remus and Sirius go running off, Severus escorts Harry to the castle, to the Hospital Wing. Eventually, Professor Dumbledore visits Harry and Harry gives him the rat - and the story about rat-Pettigrew. Even so, the dementors want to perform the kiss on Sirius because they don't really care about guilty vs. innocent.
So, then, there's the Hermione and Harry going back in time thing, to save Buckbeak and rescue Sirius from the tower. During this, Hermione howls like a wolf (saving Harry and Severus from Remus) and Harry saves Sirius (with his patronus) from the dementors before they rescue him from the tower.
The following day it's announced via the Daily Prophet that Sirius was innocent all along and Pettigrew was an Animagus, and then there's a few more days of term in which Harry says goodbye to Remus (who chose to resign). Then, Harry goes to the Dursleys for two weeks. During that time, Sirius is exonerated. It's another week before Grimmauld Place is livable.
Which leads us to the start of our story. :)